AI-NeuralNet-Mesh
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Revision history for Perl extension AI::NeuralNet::Mesh.
0.20 Tue Aug 22 18:01:04 2000
- Original version; created by Josiah Bryan
- Complete core re-write of AI::NeuralNet::BackProp
- 23% More accuracy in learning
- Increased learning speed
- Better connection topology
0.31 Fri Aug 25 05:10:11 20000
- Second release, by Josiah Bryan
- 3 Major features:
- seperate layer sizes
- custom node activations
- increased learning speed
0.43 Wed Sep 14 03:13:01 20000
- Third release, by Josiah Bryan
- Several bug fixes
- fixed 'flag' option on learn_set()
- fixed multiple-output bug
- fixed learning gradient error
- Improved learning function to not degrade increment automatically
- Added CSV-style dataset loader
- Added Export tags
- Added four custom node activations, including range and ramp
- Added several misc. extra functions
- Added ALN example demo
Makefile.PL view on Meta::CPAN
use ExtUtils::MakeMaker;
# See lib/ExtUtils/MakeMaker.pm for details of how to influence
# the contents of the Makefile that is written.
WriteMakefile(
'NAME' => 'AI::NeuralNet::Mesh',
'VERSION_FROM' => 'Mesh.pm', # finds $VERSION
'PREREQ_PM' => {},
);
#!/usr/bin/perl
# Copyright (c) 2000 Josiah Bryan USA
#
# See AUTHOR section in pod text below for usage and distribution rights.
#
BEGIN {
$AI::NeuralNet::Mesh::VERSION = "0.44";
$AI::NeuralNet::Mesh::ID =
'$Id: AI::NeuralNet::Mesh.pm, v'.$AI::NeuralNet::Mesh::VERSION.' 2000/15/09 03:29:08 josiah Exp $';
}
package AI::NeuralNet::Mesh;
require Exporter;
@ISA = qw(Exporter);
@EXPORT = qw(range intr pdiff);
%EXPORT_TAGS = (
'default' => [ qw ( range intr pdiff )],
'all' => [ qw ( p low high ramp and_gate or_gate range intr pdiff ) ],
'p' => [ qw ( p low high intr pdiff ) ],
'acts' => [ qw ( ramp and_gate or_gate range ) ],
);
@EXPORT_OK = ( @{ $EXPORT_TAGS{'all'} }, qw( p low high ramp and_gate or_gate ) );
use strict;
use Benchmark;
# See POD for usage of this variable.
$AI::NeuralNet::Mesh::Connector = '_c';
# Debugging subs
$AI::NeuralNet::Mesh::DEBUG = 0;
sub whowasi { (caller(1))[3] . '()' }
sub debug { shift; $AI::NeuralNet::Mesh::DEBUG = shift || 0; }
sub d { shift if(substr($_[0],0,4) eq 'AI::'); my ($a,$b,$c)=(shift,shift,$AI::NeuralNet::Mesh::DEBUG); print $a if($c == $b); return $c }
sub verbose {debug @_};
sub verbosity {debug @_};
sub v {debug @_};
# Return version of ::ID string passed or current version of this
# module if no string is passed. Used in load() to detect file versions.
sub version {
shift if(substr($_[0],0,4) eq 'AI::');
substr((split(/\s/,(shift || $AI::NeuralNet::Mesh::ID)))[2],1);
}
# Rounds a floating-point to an integer with int() and sprintf()
sub intr {
shift if(substr($_[0],0,4) eq 'AI::');
try { return int(sprintf("%.0f",shift)) }
catch { return 0 }
}
# Package constructor
sub new {
no strict 'refs';
my $type = shift;
my $self = {};
my $layers = shift;
my $nodes = shift;
my $outputs = shift || $nodes;
my $inputs = shift || $nodes;
bless $self, $type;
# If $layers is a string, then it will be numerically equal to 0, so
# try to load it as a network file.
if($layers == 0) {
# We use a "1" flag as the second argument to indicate that we
# want load() to call the new constructor to make a network the
# same size as in the file and return a refrence to the network,
# instead of just creating the network from pre-exisiting refrence
return $self->load($layers,1);
}
# Looks like we got ourselves a layer specs array
if(ref($layers) eq "ARRAY") {
if(ref($layers->[0]) eq "HASH") {
$self->{total_nodes} = 0;
$self->{inputs} = $layers->[0]->{nodes};
$self->{nodes} = $layers->[0]->{nodes};
$self->{outputs} = $layers->[$#{$layers}]->{nodes};
$self->{total_layers} = $#{$layers};
for (0..$#{$layers}){$self->{layers}->[$_] = $layers->[$_]->{nodes}}
for (0..$self->{total_layers}){$self->{total_nodes}+=$self->{layers}->[$_]}
} else {
$self->{inputs} = $layers->[0];
$self->{nodes} = $layers->[0];
$self->{outputs} = $layers->[$#{$layers}];
$self->{layers} = $layers;
$self->{total_layers} = $#{$self->{layers}};
$self->{total_nodes} = 0;
for (0..$self->{total_layers}) {
$self->{total_nodes}+=$self->{layers}->[$_];
}
}
} else {
$self->{total_nodes} = $layers * $nodes + $outputs;
$self->{total_layers} = $layers;
$self->{nodes} = $nodes;
$self->{inputs} = $inputs;
$self->{outputs} = $outputs;
}
# Initalize misc. variables
$self->{col_width} = 5;
$self->{random} = 0;
$self->{const} = 0.0001;
$self->{connector} = $AI::NeuralNet::Mesh::Connector;
# Build mesh
$self->_init();
# Initalize activation, thresholds, etc, if provided
if(ref($layers->[0]) eq "HASH") {
for (0..$self->{total_layers}) {
$self->activation($_,$layers->[$_]->{activation});
$self->threshold($_,$layers->[$_]->{threshold});
$self->mean($_,$layers->[$_]->{mean});
}
}
# Done!
return $self;
}
# Internal usage
# Connects one range of nodes to another range
sub _c {
my $self = shift;
my $r1a = shift;
my $r1b = shift;
my $r2a = shift;
my $r2b = shift;
my $m1 = shift || $self->{mesh};
my $m2 = shift || $m1;
for my $y ($r1a..$r1b-1) {
for my $z ($r2a..$r2b-1) {
$m1->[$y]->add_output_node($m2->[$z]);
}
}
}
# Internal usage
# Creates the mesh of neurons
sub _init {
my $self = shift;
my $nodes = $self->{nodes};
my $outputs = $self->{outputs} || $nodes;
my $inputs = $self->{inputs} || $nodes;
my $layers = $self->{total_layers};
my $tmp = $self->{total_nodes} || ($layers * $nodes + $outputs);
my $layer_specs = $self->{layers};
my $connector = $self->{connector};
my ($x,$y,$z);
no strict 'refs';
# Just to be safe.
$self->{total_nodes} = $tmp;
# If they didn't give layer specifications, then we derive our own specs.
if(!(defined $self->{layers})) {
$layer_specs = [split(',',"$nodes," x $layers)];
$layer_specs->[$#{$layer_specs}+1]=$outputs;
$self->{layers} = $layer_specs;
}
# First create the individual nodes
for my $x (0..$tmp-1) {
$self->{mesh}->[$x] = AI::NeuralNet::Mesh::node->new($self);
}
# Get an instance of an output (data collector) node
$self->{output} = AI::NeuralNet::Mesh::output->new($self);
# Connect the output layer to the data collector
for $x (0..$outputs-1) {
$self->{mesh}->[$tmp-$outputs+$x]->add_output_node($self->{output});
}
# Now we use the _c() method to connect the layers together.
$y=0;
my $c = $connector.'($self,$y,$y+$z,$y+$z,$y+$z+$layer_specs->[$x+1])';
for $x (0..$layers-1) {
$z = $layer_specs->[$x];
d("layer $x size: $z (y:$y)\n,",1);
eval $c;
$y+=$z;
}
# Get an instance of our cap node.
$self->{input}->{cap} = AI::NeuralNet::Mesh::cap->new();
# Add a cap to the bottom of the mesh to stop it from trying
# to recursivly adjust_weight() where there are no more nodes.
for my $x (0..$inputs-1) {
$self->{input}->{IDs}->[$x] =
$self->{mesh}->[$x]->add_input_node($self->{input}->{cap});
}
}
# See POD for usage
sub extend {
my $self = shift;
my $layers = shift;
# Looks like we got ourselves a layer specs array
if(ref($layers) eq "ARRAY") {
if($self->{total_layers}!=$#{$layers}) {
$self->{error} = "extend(): Cannot add new layers. Create a new network to add layers.\n";
return undef;
}
if(ref($layers->[0]) eq "HASH") {
$self->{total_nodes} = 0;
$self->{inputs} = $layers->[0]->{nodes};
$self->{nodes} = $layers->[0]->{nodes};
$self->{outputs} = $layers->[$#{$layers}]->{nodes};
for (0..$#{$layers}){
$self->extend_layer($_,$layers->[$_]);
$self->{layers}->[$_] =$layers->[$_]->{nodes};
}
for (0..$self->{total_layers}){$self->{total_nodes}+=$self->{layers}->[$_]}
} else {
$self->{inputs} = $layers->[0];
$self->{nodes} = $layers->[0];
$self->{outputs} = $layers->[$#{$layers}];
$self->{total_nodes} = 0;
for (0..$self->{total_layers}){$self->extend_layer($_,$layers->[$_])}
$self->{layers} = $layers;
for (0..$self->{total_layers}){$self->{total_nodes}+= $self->{layers}->[$_]}
}
} else {
$self->{error} = "extend(): Invalid argument type.\n";
return undef;
}
return 1;
}
# See POD for usage
sub extend_layer {
my $self = shift;
my $layer = shift || 0;
my $specs = shift;
if(!$specs) {
$self->{error} = "extend_layer(): You must provide specs to extend layer $layer with.\n";
return undef;
}
if(ref($specs) eq "HASH") {
$self->activation($layer,$specs->{activation}) if($specs->{activation});
$self->threshold($layer,$specs->{threshold}) if($specs->{threshold});
$self->mean($layer,$specs->{mean}) if($specs->{mean});
return $self->add_nodes($layer,$specs->{nodes});
} else {
return $self->add_nodes($layer,$specs);
}
return 1;
}
# Pseudo-internal usage
sub add_nodes {
no strict 'refs';
my $self = shift;
my $layer = shift;
my $nodes = shift;
my $n = 0;
my $more = $nodes - $self->{layers}->[$layer] - 1;
d("Checking on extending layer $layer to $nodes nodes (check:$self->{layers}->[$layer]).\n",9);
return 1 if ($nodes == $self->{layers}->[$layer]);
if ($self->{layers}->[$layer]>$nodes) {
$self->{error} = "add_nodes(): I cannot remove nodes from the network with this version of my module. You must create a new network to remove nodes.\n";
return undef;
}
d("Extending layer $layer by $more.\n",9);
for (0..$more){$self->{mesh}->[$#{$self->{mesh}}+1]=AI::NeuralNet::Mesh::node->new($self)}
for(0..$layer-2){$n+=$self->{layers}->[$_]}
$self->_c($n,$n+$self->{layers}->[$layer-1],$#{$self->{mesh}}-$more+1,$#{$self->{mesh}});
$self->_c($#{$self->{mesh}}-$more+1,$#{$self->{mesh}},$n+$self->{layers}->[$layer],$n+$self->{layers}->[$layer]+$self->{layers}->[$layer+1]);
}
# See POD for usage
sub run {
my $self = shift;
my $inputs = shift;
my $const = $self->{const};
#my $start = new Benchmark;
$inputs = $self->crunch($inputs) if($inputs == 0);
no strict 'refs';
for my $x (0..$#{$inputs}) {
last if($x>$self->{inputs});
d("inputing $inputs->[$x] at index $x with ID $self->{input}->{IDs}->[$x].\n",1);
$self->{mesh}->[$x]->input($inputs->[$x]+$const,$self->{input}->{IDs}->[$x]);
}
if($#{$inputs}<$self->{inputs}-1) {
for my $x ($#{$inputs}+1..$self->{inputs}-1) {
d("inputing 1 at index $x with ID $self->{input}->{IDs}->[$x].\n",1);
$self->{mesh}->[$x]->input(1,$self->{input}->{IDs}->[$x]);
}
}
#$self->{benchmark} = timestr(timediff(new Benchmark, $start));
return $self->{output}->get_outputs();
}
# See POD for usage
sub run_uc {
$_[0]->uncrunch(run(@_));
}
# See POD for usage
sub learn {
my $self = shift;
my $inputs = shift; # input set
my $outputs = shift; # target outputs
my %args = @_; # get args into hash
my $inc = $args{inc} || 0.002; # learning gradient
my $max = $args{max} || 1024; # max iteterations
my $degrade = $args{degrade} || 0; # enable gradient degrading
my $error = ($args{error}>-1 && defined $args{error}) ? $args{error} : -1;
my $dinc = 0.0002; # amount to adjust gradient by
my $diff = 100; # error magin between results
my $start = new Benchmark;
$inputs = $self->crunch($inputs) if($inputs == 0);
$outputs = $self->crunch($outputs) if($outputs == 0);
my ($flag,$ldiff,$cdiff,$_mi,$loop,$y);
while(!$flag && ($max ? $loop<$max : 1)) {
my $b = new Benchmark;
my $got = $self->run($inputs);
$diff = pdiff($got,$outputs);
$flag = 1;
if(($error>-1 ? $diff<$error : 0) || !$diff) {
$flag=1;
last;
}
if($degrade) {
$inc -= ($dinc*$diff);
if($diff eq $ldiff) {
$cdiff++;
$inc += ($dinc*$diff)+($dinc*$cdiff*10);
} else {
$cdiff=0;
}
$ldiff = $diff;
}
for my $x (0..$self->{outputs}-1) {
my $a = $got->[$x];
my $b = $outputs->[$x];
d("got: $a, wanted: $b\n",2);
if ($a != $b) {
$flag = 0;
$y = $self->{total_nodes}-$self->{outputs}+$x;
$self->{mesh}->[$y]->adjust_weight(($a<$b?1:-1)*$inc,$b);
}
}
$loop++;
d("===============================Loop: [$loop]===================================\n",4);
d("Current Error: $diff\tCurrent Increment: $inc\n",4);
d("Benchmark: ".timestr(timediff(new Benchmark,$b))."\n",4);
d("============================Results, [$loop]===================================\n",4);
d("Actual: ",4);
join_cols($got,($self->{col_width})?$self->{col_width}:5) if(d()==4);
d("Target: ",4);
join_cols($outputs,($self->{col_width})?$self->{col_width}:5) if(d()==4);
d("\n",4);
d('.',12);
d('['.join(',',@{$got})."-".join(',',@{$outputs}).']',13);
}
my $str = "Learning took $loop loops and ".timestr(timediff(new Benchmark,$start))."\n";
d($str,3); $self->{benchmark} = "$loop loops and ".timestr(timediff(new Benchmark,$start))."\n";
return $str;
}
# See POD for usage
sub learn_set {
my $self = shift;
my $data = shift;
my %args = @_;
my $len = $#{$data}/2;
my $inc = $args{inc};
my $max = $args{max};
my $error = $args{error};
my $degrade = $args{degrade};
my $p = (defined $args{flag}) ?$args{flag} :1;
my $row = (defined $args{row}) ?$args{row}+1:1;
my $leave = (defined $args{leave})?$args{leave}:0;
for my $x (0..$len-$leave) {
d("Learning set $x...\n",4);
my $str = $self->learn( $data->[$x*2],
$data->[$x*2+1],
inc=>$inc,
max=>$max,
error=>$error,
degrade=>$degrade);
}
if ($p) {
return pdiff($data->[$row],$self->run($data->[$row-1]));
} else {
return $data->[$row]->[0]-$self->run($data->[$row-1])->[0];
}
}
# See POD for usage
sub run_set {
my $self = shift;
my $data = shift;
my $len = $#{$data}/2;
my (@results,$res);
for my $x (0..$len) {
$res = $self->run($data->[$x*2]);
for(0..$#{$res}){$results[$x]->[$_]=$res->[$_]}
d("Running set $x [$res->[0]]...\r",4);
}
return \@results;
}
#
# Loads a CSV-like dataset from disk
#
# Usage:
# my $set = $set->load_set($file, $column, $seperator);
#
# Returns a data set of the same format as required by the
# learn_set() method. $file is the disk file to load set from.
# $column an optional variable specifying the column in the
# data set to use as the class attribute. $class defaults to 0.
# $seperator is an optional variable specifying the seperator
# character between values. $seperator defaults to ',' (a single comma).
# NOTE: This does not handle quoted fields, or any other record
# seperator other than "\n".
#
sub load_set {
my $self = shift;
my $file = shift;
my $attr = shift || 0;
my $sep = shift || ',';
my $data = [];
open(FILE, $file);
my @lines = <FILE>;
close(FILE);
for my $x (0..$#lines) {
chomp($lines[$x]);
my @tmp = split /$sep/, $lines[$x];
my $c=0;
for(0..$#tmp){
$tmp[$_]=$self->crunch($tmp[$_])->[0] if($tmp[$_]=~/[AaBbCcDdEeFfGgHhIiJjKkLlMmNnOoPpQqRrSsTtUuVvWwXxYyZz]/);
if($_!=$attr){$data->[$x*2]->[$c]=$tmp[$c];$c++}
};
d("Loaded line $x, [@tmp] \r",4);
$data->[$x*2+1]=[$tmp[$attr]];
}
return $data;
}
# See POD for usage
sub get_outs {
my $self = shift;
my $data = shift;
my $len = $#{$data}/2;
my $outs = [];
for my $x (0..$len) {
$outs->[$x] = $data->[$x*2+1];
}
return $outs;
}
# Save entire network state to disk.
sub save {
my $self = shift;
my $file = shift;
no strict 'refs';
open(FILE,">$file");
print FILE "header=$AI::NeuralNet::Mesh::ID\n";
print FILE "total_layers=$self->{total_layers}\n";
print FILE "total_nodes=$self->{total_nodes}\n";
print FILE "nodes=$self->{nodes}\n";
print FILE "inputs=$self->{inputs}\n";
print FILE "outputs=$self->{outputs}\n";
print FILE "layers=",(($self->{layers})?join(',',@{$self->{layers}}):''),"\n";
print FILE "rand=$self->{random}\n";
print FILE "const=$self->{const}\n";
print FILE "cw=$self->{col_width}\n";
print FILE "crunch=$self->{_crunched}->{_length}\n";
print FILE "rA=$self->{rA}\n";
print FILE "rB=$self->{rB}\n";
print FILE "rS=$self->{rS}\n";
print FILE "rRef=",(($self->{rRef})?join(',',@{$self->{rRef}}):''),"\n";
for my $a (0..$self->{_crunched}->{_length}-1) {
print FILE "c$a=$self->{_crunched}->{list}->[$a]\n";
}
my $n = 0;
for my $x (0..$self->{total_layers}) {
for my $y (0..$self->{layers}->[$x]-1) {
my $w='';
for my $z (0..$self->{layers}->[$x-1]-1) {
$w.="$self->{mesh}->[$n]->{_inputs}->[$z]->{weight},";
}
print FILE "n$n=$w$self->{mesh}->[$n]->{activation},$self->{mesh}->[$n]->{threshold},$self->{mesh}->[$n]->{mean}\n";
$n++;
}
}
close(FILE);
if(!(-f $file)) {
$self->{error} = "Error writing to \"$file\".";
return undef;
}
return $self;
}
# Load entire network state from disk.
sub load {
my $self = shift;
my $file = shift;
my $load_flag = shift;
my @lines;
if(-f $file) {
open(FILE,"$file");
@lines=<FILE>;
close(FILE);
} else {
@lines=split /\n/, $file;
}
my %db;
for my $line (@lines) {
chomp($line);
my ($a,$b) = split /=/, $line;
$db{$a}=$b;
}
if(!$db{"header"}) {
$self->{error} = "Invalid format.";
return undef;
}
return $self->load_old($file) if($self->version($db{"header"})<0.21);
if($load_flag) {
undef $self;
$self = AI::NeuralNet::Mesh->new([split(',',$db{layers})]);
} else {
$self->{inputs} = $db{inputs};
$self->{nodes} = $db{nodes};
$self->{outputs} = $db{outputs};
$self->{layers} = [split(',',$db{layers})];
$self->{total_layers} = $db{total_layers};
$self->{total_nodes} = $db{total_nodes};
}
# Load variables
$self->{random} = $db{"rand"};
$self->{const} = $db{"const"};
$self->{col_width} = $db{"cw"};
$self->{rA} = $db{"rA"};
$self->{rB} = $db{"rB"};
$self->{rS} = $db{"rS"};
$self->{rRef} = [split /\,/, $db{"rRef"}];
$self->{_crunched}->{_length} = $db{"crunch"};
for my $a (0..$self->{_crunched}->{_length}-1) {
$self->{_crunched}->{list}->[$a] = $db{"c$a"};
}
$self->_init();
my $n = 0;
for my $x (0..$self->{total_layers}) {
for my $y (0..$self->{layers}->[$x]-1) {
my @l = split /\,/, $db{"n$n"};
for my $z (0..$self->{layers}->[$x-1]-1) {
$self->{mesh}->[$n]->{_inputs}->[$z]->{weight} = $l[$z];
}
my $z = $self->{layers}->[$x-1];
$self->{mesh}->[$n]->{activation} = $l[$z];
$self->{mesh}->[$n]->{threshold} = $l[$z+1];
$self->{mesh}->[$n]->{mean} = $l[$z+2];
$n++;
}
}
return $self;
}
# Load entire network state from disk.
sub load_old {
my $self = shift;
my $file = shift;
my $load_flag = shift;
if(!(-f $file)) {
$self->{error} = "File \"$file\" does not exist.";
return undef;
}
open(FILE,"$file");
my @lines=<FILE>;
close(FILE);
my %db;
for my $line (@lines) {
chomp($line);
my ($a,$b) = split /=/, $line;
$db{$a}=$b;
}
if(!$db{"header"}) {
$self->{error} = "Invalid format.";
return undef;
}
if($load_flag) {
undef $self;
# Create new network
$self = AI::NeuralNet::Mesh->new($db{"layers"},
$db{"nodes"},
$db{"outputs"});
} else {
$self->{total_layers} = $db{"layers"};
$self->{nodes} = $db{"nodes"};
$self->{outputs} = $db{"outputs"};
$self->{inputs} = $db{"nodes"};
#$self->{total_nodes} = $db{"total"};
}
# Load variables
$self->{random} = $db{"rand"};
$self->{const} = $db{"const"};
$self->{col_width} = $db{"cw"};
$self->{rA} = $db{"rA"};
$self->{rB} = $db{"rB"};
$self->{rS} = $db{"rS"};
$self->{rRef} = [split /\,/, $db{"rRef"}];
$self->{_crunched}->{_length} = $db{"crunch"};
for my $a (0..$self->{_crunched}->{_length}-1) {
$self->{_crunched}->{list}->[$a] = $db{"c$a"};
}
$self->_init();
my $nodes = $self->{nodes};
my $outputs = $self->{outputs};
my $tmp = $self->{total_nodes};
my $div = intr($nodes/$outputs);
# Load input and hidden
for my $a (0..$tmp-1) {
my @l = split /\,/, $db{"n$a"};
for my $b (0..$nodes-1) {
$self->{mesh}->[$a]->{_inputs}->[$b]->{weight} = $l[$b];
}
}
# Load output layer
for my $x (0..$outputs-1) {
my @l = split /\,/, $db{"n".($tmp+$x)};
for my $y (0..$div-1) {
$self->{mesh}->[$tmp+$x]->{_inputs}->[$y]->{weight} = $l[$y];
}
}
return $self;
}
# Dumps the complete weight matrix of the network to STDIO
sub show {
my $self = shift;
my $n = 0;
no strict 'refs';
for my $x (0..$self->{total_layers}) {
for my $y (0..$self->{layers}->[$x]-1) {
for my $z (0..$self->{layers}->[$x-1]-1) {
print "$self->{mesh}->[$n]->{_inputs}->[$z]->{weight},";
}
$n++;
}
print "\n";
}
}
# Set the activation type of a specific layer.
# usage: $net->activation($layer,$type);
# $type can be: "linear", "sigmoid", "sigmoid_2".
# You can use "sigmoid_1" as a synonym to "sigmoid".
# Type can also be a CODE ref, ( ref($type) eq "CODE" ).
# If $type is a CODE ref, then the function is called in this form:
# $output = &$type($sum_of_inputs,$self);
# The code ref then has access to all the data in that node (thru the
# blessed refrence $self) and is expected to return the value to be used
# as the output for that node. The sum of all the inputs to that node
# is already summed and passed as the first argument.
sub activation {
my $self = shift;
my $layer = shift || 0;
my $value = shift || 'linear';
my $n = 0;
no strict 'refs';
for(0..$layer-1){$n+=$self->{layers}->[$_]}
for($n..$n+$self->{layers}->[$layer]-1) {
$self->{mesh}->[$_]->{activation} = $value;
}
}
# Applies an activation type to a specific node
sub node_activation {
my $self = shift;
my $layer = shift || 0;
my $node = shift || 0;
my $value = shift || 'linear';
my $n = 0;
no strict 'refs';
for(0..$layer-1){$n+=$self->{layers}->[$_]}
$self->{mesh}->[$n+$node]->{activation} = $value;
}
# Set the activation threshold for a specific layer.
# Only applicable if that layer uses "sigmoid" or "sigmoid_2"
# usage: $net->threshold($layer,$threshold);
sub threshold {
my $self = shift;
my $layer = shift || 0;
my $value = shift || 0.5;
my $n = 0;
no strict 'refs';
for(0..$layer-1){$n+=$self->{layers}->[$_]}
for($n..$n+$self->{layers}->[$layer]-1) {
$self->{mesh}->[$_]->{threshold} = $value;
}
}
# Applies a threshold to a specific node
sub node_threshold {
my $self = shift;
my $layer = shift || 0;
my $node = shift || 0;
my $value = shift || 0.5;
my $n = 0;
no strict 'refs';
for(0..$layer-1){$n+=$self->{layers}->[$_]}
$self->{mesh}->[$n+$node]->{threshold} = $value;
}
# Set mean (avg.) flag for a layer.
# usage: $net->mean($layer,$flag);
# If $flag is true, it enables finding the mean for that layer,
# If $flag is false, disables mean.
sub mean {
my $self = shift;
my $layer = shift || 0;
my $value = shift || 0;
my $n = 0;
no strict 'refs';
for(0..$layer-1){$n+=$self->{layers}->[$_]}
for($n..$n+$self->{layers}->[$layer]-1) {
$self->{mesh}->[$_]->{mean} = $value;
}
}
# Returns a pcx object
sub load_pcx {
my $self = shift;
my $file = shift;
eval('use PCX::Loader');
if(@_) {
$self->{error}="Cannot load PCX::Loader module: @_";
return undef;
}
return PCX::Loader->new($self,$file);
}
# Crunch a string of words into a map
sub crunch {
my $self = shift;
my @ws = split(/[\s\t]/,shift);
my (@map,$ic);
for my $a (0..$#ws) {
$ic=$self->crunched($ws[$a]);
if(!defined $ic) {
$self->{_crunched}->{list}->[$self->{_crunched}->{_length}++]=$ws[$a];
$map[$a]=$self->{_crunched}->{_length};
} else {
$map[$a]=$ic;
}
}
return \@map;
}
# Finds if a word has been crunched.
# Returns undef on failure, word index for success.
sub crunched {
my $self = shift;
for my $a (0..$self->{_crunched}->{_length}-1) {
return $a+1 if($self->{_crunched}->{list}->[$a] eq $_[0]);
}
$self->{error} = "Word \"$_[0]\" not found.";
return undef;
}
# Alias for crunched(), above
sub word { crunched(@_) }
# Uncrunches a map (array ref) into an array of words (not an array ref)
# and returns array
sub uncrunch {
my $self = shift;
my $map = shift;
my ($c,$el,$x);
foreach $el (@{$map}) {
$c .= $self->{_crunched}->{list}->[$el-1].' ';
}
return $c;
}
# Sets/gets randomness facter in the network. Setting a value of 0
# disables random factors.
sub random {
my $self = shift;
my $rand = shift;
return $self->{random} if(!(defined $rand));
$self->{random} = $rand;
}
# Sets/gets column width for printing lists in debug modes 1,3, and 4.
sub col_width {
my $self = shift;
my $width = shift;
return $self->{col_width} if(!$width);
$self->{col_width} = $width;
}
# Sets/gets run const. facter in the network. Setting a value of 0
# disables run const. factor.
sub const {
my $self = shift;
my $const = shift;
return $self->{const} if(!(defined $const));
$self->{const} = $const;
}
# Return benchmark time from last learn() operation.
sub benchmark {
shift->{benchmarked};
}
# Same as benchmark()
sub benchmarked {
benchmark(shift);
}
# Return the last error in the mesh, or undef if no error.
sub error {
my $self = shift;
return undef if !$self->{error};
chomp($self->{error});
return $self->{error}."\n";
}
# Used to format array ref into columns
# Usage:
# join_cols(\@array,$row_length_in_elements,$high_state_character,$low_state_character);
# Can also be called as method of your neural net.
# If $high_state_character is null, prints actual numerical values of each element.
sub join_cols {
no strict 'refs';
shift if(substr($_[0],0,4) eq 'AI::');
my $map = shift;
my $break = shift;
my $a = shift;
my $b = shift;
my $x;
foreach my $el (@{$map}) {
my $str = ((int($el))?$a:$b);
$str=$el."\0" if(!$a);
print $str; $x++;
if($x>$break-1) { print "\n"; $x=0; }
}
print "\n";
}
# Returns percentage difference between all elements of two
# array refs of exact same length (in elements).
# Now calculates actual difference in numerical value.
sub pdiff {
no strict 'refs';
shift if(substr($_[0],0,4) eq 'AI::');
my $a1 = shift;
my $a2 = shift;
my $a1s = $#{$a1};
my $a2s = $#{$a2};
my ($a,$b,$diff,$t);
$diff=0;
for my $x (0..$a1s) {
$a = $a1->[$x]; $b = $a2->[$x];
if($a!=$b) {
if($a<$b){$t=$a;$a=$b;$b=$t;}
$a=1 if(!$a); $diff+=(($a-$b)/$a)*100;
}
}
$a1s = 1 if(!$a1s);
return sprintf("%.10f",($diff/$a1s));
}
# Returns $fa as a percentage of $fb
sub p {
shift if(substr($_[0],0,4) eq 'AI::');
my ($fa,$fb)=(shift,shift);
sprintf("%.3f",$fa/$fb*100); #((($fb-$fa)*((($fb-$fa)<0)?-1:1))/$fa)*100
}
# Returns the index of the element in array REF passed with the highest
# comparative value
sub high {
shift if(substr($_[0],0,4) eq 'AI::');
my $ref1 = shift; my ($el,$len,$tmp); $tmp=0;
foreach $el (@{$ref1}) { $len++ }
for my $x (0..$len-1) { $tmp = $x if($ref1->[$x] > $ref1->[$tmp]) }
return $tmp;
}
# Returns the index of the element in array REF passed with the lowest
# comparative value
sub low {
shift if(substr($_[0],0,4) eq 'AI::');
my $ref1 = shift; my ($el,$len,$tmp); $tmp=0;
foreach $el (@{$ref1}) { $len++ }
for my $x (0..$len-1) { $tmp = $x if($ref1->[$x] < $ref1->[$tmp]) }
return $tmp;
}
# Following is a collection of a few nifty custom activation functions.
# range() is exported by default, the rest you can get with:
# use AI::NeuralNet::Mesh ':acts'
# The ':all' tag also gets these into your namespace.
#
# range() returns a closure limiting the output
# of that node to a specified set of values.
# Good for output layers.
#
# usage example:
# $net->activation(4,range(0..5));
# or:
# ..
# {
# nodes => 1,
# activation => range 5..2
# }
# ..
# You can also pass an array containing the range
# values (not array ref), or you can pass a comma-
# seperated list of values as parameters:
#
# $net->activation(4,range(@numbers));
# $net->activation(4,range(6,15,26,106,28,3));
#
# Note: when using a range() activatior, train the
# net TWICE on the data set, because the first time
# the range() function searches for the top value in
# the inputs, and therefore, results could flucuate.
# The second learning cycle guarantees more accuracy.
#
sub range {
my @r=@_;
sub{$_[1]->{t}=$_[0]if($_[0]>$_[1]->{t});$r[intr($_[0]/$_[1]->{t}*$#r)]}
}
#
# ramp() preforms smooth ramp activation between 0 and 1 if $r is 1,
# or between -1 and 1 if $r is 2. $r defaults to 1, as you can see.
#
# Note: when using a ramp() activatior, train the
# net at least TWICE on the data set, because the first
# time the ramp() function searches for the top value in
# the inputs, and therefore, results could flucuate.
# The second learning cycle guarantees more accuracy.
#
sub ramp {
my $r=shift||1;my $t=($r<2)?0:-1;
sub{$_[1]->{t}=$_[0]if($_[0]>$_[1]->{t});$_[0]/$_[1]->{t}*$r-$b}
}
# Self explanitory, pretty much. $threshold is used to decide if an input
# is true or false (1 or 0). If an input is below $threshold, it is false.
sub and_gate {
my $threshold = shift || 0.5;
sub {
my $sum = shift;
my $self = shift;
for my $x (0..$self->{_inputs_size}-1) { return $self->{_parent}->{const} if!$self->{_inputs}->[$x]->{value}<$threshold }
return $sum/$self->{_inputs_size};
}
}
# Self explanitory, $threshold is used same as above.
sub or_gate {
my $threshold = shift || 0.5;
sub {
my $sum = shift;
my $self = shift;
for my $x (0..$self->{_inputs_size}-1) { return $sum/$self->{_inputs_size} if!$self->{_inputs}->[$x]->{value}<$threshold }
return $self->{_parent}->{const};
}
}
1;
package AI::NeuralNet::Mesh::node;
use strict;
# Node constructor
sub new {
my $type = shift;
my $self ={
_parent => shift,
_inputs => [],
_outputs => []
};
bless $self, $type;
}
# Receive inputs from other nodes, and also send
# outputs on.
sub input {
my $self = shift;
my $input = shift;
my $from_id = shift;
$self->{_inputs}->[$from_id]->{value} = $input * $self->{_inputs}->[$from_id]->{weight};
$self->{_inputs}->[$from_id]->{input} = $input;
$self->{_inputs}->[$from_id]->{fired} = 1;
$self->{_parent}->d("got input $input from id $from_id, weighted to $self->{_inputs}->[$from_id]->{value}.\n",1);
my $flag = 1;
for my $x (0..$self->{_inputs_size}-1) { $flag = 0 if(!$self->{_inputs}->[$x]->{fired}) }
if ($flag) {
$self->{_parent}->d("all inputs fired for $self.\n",1);
my $output = 0;
# Sum
for my $i (@{$self->{_inputs}}) {
$output += $i->{value};
}
# Handle activations, thresholds, and means
$output /= $self->{_inputs_size} if($self->{flag_mean});
#$output += (rand()*$self->{_parent}->{random});
$output = ($output>=$self->{threshold})?1:0 if(($self->{activation} eq "sigmoid") || ($self->{activation} eq "sigmoid_1"));
if($self->{activation} eq "sigmoid_2") {
$output = 1 if($output >$self->{threshold});
$output = -1 if($output <$self->{threshold});
$output = 0 if($output==$self->{threshold});
}
# Handle CODE refs
$output = &{$self->{activation}}($output,$self) if(ref($self->{activation}) eq "CODE");
# Send output
for my $o (@{$self->{_outputs}}) { $o->{node}->input($output,$o->{from_id}) }
} else {
$self->{_parent}->d("all inputs have NOT fired for $self.\n",1);
}
}
sub add_input_node {
my $self = shift;
my $node = shift;
my $i = $self->{_inputs_size} || 0;
$self->{_inputs}->[$i]->{node} = $node;
$self->{_inputs}->[$i]->{value} = 0;
$self->{_inputs}->[$i]->{weight} = 1; #rand()*1;
$self->{_inputs}->[$i]->{fired} = 0;
$self->{_inputs_size} = ++$i;
return $i-1;
}
sub add_output_node {
my $self = shift;
my $node = shift;
my $i = $self->{_outputs_size} || 0;
$self->{_outputs}->[$i]->{node} = $node;
$self->{_outputs}->[$i]->{from_id} = $node->add_input_node($self);
$self->{_outputs_size} = ++$i;
return $i-1;
}
sub adjust_weight {
my $self = shift;
my $inc = shift;
for my $i (@{$self->{_inputs}}) {
$i->{weight} += $inc * $i->{weight};
$i->{node}->adjust_weight($inc) if($i->{node});
}
}
1;
# Internal usage, prevents recursion on empty nodes.
package AI::NeuralNet::Mesh::cap;
sub new { bless {}, shift }
sub input {}
sub adjust_weight {}
sub add_output_node {}
sub add_input_node {}
1;
# Internal usage, collects data from output layer.
package AI::NeuralNet::Mesh::output;
use strict;
sub new {
my $type = shift;
my $self ={
_parent => shift,
_inputs => [],
};
bless $self, $type;
}
sub add_input_node {
my $self = shift;
return (++$self->{_inputs_size})-1;
}
sub input {
my $self = shift;
my $input = shift;
my $from_id = shift;
$self->{_parent}->d("GOT INPUT [$input] FROM [$from_id]\n",1);
$self->{_inputs}->[$from_id] = $self->{_parent}->intr($input);
}
sub get_outputs {
my $self = shift;
return $self->{_inputs};
}
1;
__END__
=head1 NAME
AI::NeuralNet::Mesh - An optimized, accurate neural network Mesh.
=head1 SYNOPSIS
use AI::NeuralNet::Mesh;
# Create a mesh with 2 layers, 2 nodes/layer, and one output node.
my $net = new AI::NeuralNet::Mesh(2,2,1);
# Teach the network the AND function
$net->learn([0,0],[0]);
$net->learn([0,1],[0]);
$net->learn([1,0],[0]);
$net->learn([1,1],[1]);
# Present it with two test cases
my $result_bit_1 = $net->run([0,1])->[0];
my $result_bit_2 = $net->run([1,1])->[0];
# Display the results
print "AND test with inputs (0,1): $result_bit_1\n";
print "AND test with inputs (1,1): $result_bit_2\n";
=head1 VERSION & UPDATES
This is version B<0.44>, an update release for version 0.43.
This fixed the usage conflict with perl 5.3.3.
With this version I have gone through and tuned up many area
of this module, including the descent algorithim in learn(),
as well as four custom activation functions, and several export
tag sets. With this release, I have also included a few
new and more practical example scripts. (See ex_wine.pl) This release
also includes a simple example of an ALN (Adaptive Logic Network) made
with this module. See ex_aln.pl. Also in this release is support for
loading data sets from simple CSV-like files. See the load_set() method
for details. This version also fixes a big bug that I never knew about
until writing some demos for this version - that is, when trying to use
more than one output node, the mesh would freeze in learning. But, that
is fixed now, and you can have as many outputs as you want (how does 3
inputs and 50 outputs sound? :-)
=head1 DESCRIPTION
AI::NeuralNet::Mesh is an optimized, accurate neural network Mesh.
It was designed with accruacy and speed in mind.
This network model is very flexable. It will allow for clasic binary
operation or any range of integer or floating-point inputs you care
to provide. With this you can change activation types on a per node or
per layer basis (you can even include your own anonymous subs as
activation types). You can add sigmoid transfer functions and control
the threshold. You can learn data sets in batch, and load CSV data
set files. You can do almost anything you need to with this module.
This code is deigned to be flexable. Any new ideas for this module?
See AUTHOR, below, for contact info.
This module is designed to also be a customizable, extensable
neural network simulation toolkit. Through a combination of setting
the $Connection variable and using custom activation functions, as
well as basic package inheritance, you can simulate many different
types of neural network structures with very little new code written
by you.
In this module I have included a more accurate form of "learning" for the
mesh. This form preforms descent toward a local error minimum (0) on a
directional delta, rather than the desired value for that node. This allows
for better, and more accurate results with larger datasets. This module also
uses a simpler recursion technique which, suprisingly, is more accurate than
the original technique that I've used in other ANNs.
=head1 EXPORTS
This module exports three functions by default:
range
intr
pdiff
See range() intr() and pdiff() for description of their respective functions.
Also provided are several export tag sets for usage in the form of:
use AI::NeuralNet::Mesh ':tag';
Tag sets are:
:default
- These functions are always exported.
- Exports:
range()
intr()
pdiff()
:all
- Exports:
p()
high()
low()
range()
ramp()
and_gate()
or_gate()
:p
- Exports:
p()
high()
low()
:acts
- Exports:
ramp()
and_gate()
or_gate()
See the respective methods/functions for information about
each method/functions usage.
=head1 METHODS
=item AI::NeuralNet::Mesh->new();
There are four ways to construct a new network with new(). Each is detailed below.
P.S. Don't worry, the old C<new($layers, $nodes [, $outputs])> still works like always!
=item AI::NeuralNet::Mesh->new($layers, $nodes [, $outputs]);
Returns a newly created neural network from an C<AI::NeuralNet::Mesh>
object. The network will have C<$layers> number of layers in it
and it will have C<$nodes> number of nodes per layer.
There is an optional parameter of $outputs, which specifies the number
of output neurons to provide. If $outputs is not specified, $outputs
defaults to equal $size.
=item AI::NeuralNet::Mesh->new($file);
This will automatically create a new network from the file C<$file>. It will
return undef if the file was of an incorrect format or non-existant. Otherwise,
it will return a blessed refrence to a network completly restored from C<$file>.
=item AI::NeuralNet::Mesh->new(\@layer_sizes);
This constructor will make a network with the number of layers corresponding to the length
in elements of the array ref passed. Each element in the array ref passed is expected
to contain an integer specifying the number of nodes (neurons) in that layer. The first
layer ($layer_sizes[0]) is to be the input layer, and the last layer in @layer_sizes is to be
the output layer.
Example:
my $net = AI::NeuralNet::Mesh->new([2,3,1]);
Creates a network with 2 input nodes, 3 hidden nodes, and 1 output node.
=item AI::NeuralNet::Mesh->new(\@array_of_hashes);
Another dandy constructor...this is my favorite. It allows you to tailor the number of layers,
the size of the layers, the activation type (you can even add anonymous inline subs with this one),
and even the threshold, all with one array ref-ed constructor.
Example:
my $net = AI::NeuralNet::Mesh->new([
{
nodes => 2,
activation => linear
},
{
nodes => 3,
activation => sub {
my $sum = shift;
return $sum + rand()*1;
}
},
{
nodes => 1,
activation => sigmoid,
threshold => 0.75
}
]);
Interesting, eh? What you are basically passing is this:
my @info = (
{ },
{ },
{ },
...
);
You are passing an array ref who's each element is a hash refrence. Each
hash refrence, or more precisely, each element in the array refrence you are passing
to the constructor, represents a layer in the network. Like the constructor above,
the first element is the input layer, and the last is the output layer. The rest are
hidden layers.
Each hash refrence is expected to have AT LEAST the "nodes" key set to the number
of nodes (neurons) in that layer. The other two keys are optional. If "activation" is left
out, it defaults to "linear". If "threshold" is left out, it defaults to 0.50.
The "activation" key can be one of four values:
linear ( simply use sum of inputs as output )
sigmoid [ sigmoid_1 ] ( only positive sigmoid )
sigmoid_2 ( positive / 0 /negative sigmoid )
\&code_ref;
"sigmoid_1" is an alias for "sigmoid".
The code ref option allows you to have a custom activation function for that layer.
The code ref is called with this syntax:
$output = &$code_ref($sum_of_inputs, $self);
The code ref is expected to return a value to be used as the output of the node.
The code ref also has access to all the data of that node through the second argument,
a blessed hash refrence to that node.
See CUSTOM ACTIVATION FUNCTIONS for information on several included activation functions
other than the ones listed above.
Three of the activation syntaxes are shown in the first constructor above, the "linear",
"sigmoid" and code ref types.
You can also set the activation and threshold values after network creation with the
activation() and threshold() methods.
=item $net->learn($input_map_ref, $desired_result_ref [, options ]);
NOTE: learn_set() now has increment-degrading turned OFF by default. See note
on the degrade flag, below.
This will 'teach' a network to associate an new input map with a desired
result. It will return a string containg benchmarking information.
You can also specify strings as inputs and ouputs to learn, and they will be
crunched automatically. Example:
$net->learn('corn', 'cob');
Note, the old method of calling crunch on the values still works just as well.
The first two arguments may be array refs (or now, strings), and they may be
of different lengths.
Options should be written on hash form. There are three options:
inc => $learning_gradient
max => $maximum_iterations
error => $maximum_allowable_percentage_of_error
degrade => $degrade_increment_flag
$learning_gradient is an optional value used to adjust the weights of the internal
connections. If $learning_gradient is ommitted, it defaults to 0.002.
$maximum_iterations is the maximum numbers of iteration the loop should do.
It defaults to 1024. Set it to 0 if you never want the loop to quit before
the pattern is perfectly learned.
$maximum_allowable_percentage_of_error is the maximum allowable error to have. If
this is set, then learn() will return when the perecentage difference between the
actual results and desired results falls below $maximum_allowable_percentage_of_error.
If you do not include 'error', or $maximum_allowable_percentage_of_error is set to -1,
then learn() will not return until it gets an exact match for the desired result OR it
reaches $maximum_iterations.
$degrade_increment_flag is a simple flag used to allow/dissalow increment degrading
during learning based on a product of the error difference with several other factors.
$degrade_increment_flag is off by default. Setting $degrade_increment_flag to a true
value turns increment degrading on.
In previous module releases $degrade_increment_flag was not used, as increment degrading
was always on. In this release I have looked at several other network types as well
as several texts and decided that it would be better to not use increment degrading. The
option is still there for those that feel the inclination to use it. I have found some areas
that do need the degrade flag to work at a faster speed. See test.pl for an example. If
the degrade flag wasn't in test.pl, it would take a very long time to learn.
=item $net->learn_set(\@set, [ options ]);
This takes the same options as learn() (learn_set() uses learn() internally)
and allows you to specify a set to learn, rather than individual patterns.
A dataset is an array refrence with at least two elements in the array,
each element being another array refrence (or now, a scalar string). For
each pattern to learn, you must specify an input array ref, and an ouput
array ref as the next element. Example:
my @set = (
# inputs outputs
[ 1,2,3,4 ], [ 1,3,5,6 ],
[ 0,2,5,6 ], [ 0,2,1,2 ]
);
Inputs and outputs in the dataset can also be strings.
See the paragraph on measuring forgetfulness, below. There are
two learn_set()-specific option tags available:
flag => $flag
pattern => $row
If "flag" is set to some TRUE value, as in "flag => 1" in the hash of options, or if the option "flag"
is not set, then it will return a percentage represting the amount of forgetfullness. Otherwise,
learn_set() will return an integer specifying the amount of forgetfulness when all the patterns
are learned.
If "pattern" is set, then learn_set() will use that pattern in the data set to measure forgetfulness by.
If "pattern" is omitted, it defaults to the first pattern in the set. Example:
my @set = (
[ 0,1,0,1 ], [ 0 ],
[ 0,0,1,0 ], [ 1 ],
[ 1,1,0,1 ], [ 2 ], # <---
[ 0,1,1,0 ], [ 3 ]
);
If you wish to measure forgetfulness as indicated by the line with the arrow, then you would
pass 2 as the "pattern" option, as in "pattern => 2".
Now why the heck would anyone want to measure forgetfulness, you ask? Maybe you wonder how I
even measure that. Well, it is not a vital value that you have to know. I just put in a
"forgetfulness measure" one day because I thought it would be neat to know.
How the module measures forgetfulness is this: First, it learns all the patterns
in the set provided, then it will run the very first pattern (or whatever pattern
is specified by the "row" option) in the set after it has finished learning. It
will compare the run() output with the desired output as specified in the dataset.
In a perfect world, the two should match exactly. What we measure is how much that
they don't match, thus the amount of forgetfulness the network has.
Example (from examples/ex_dow.pl):
# Data from 1989 (as far as I know..this is taken from example data on BrainMaker)
my @data = (
# Mo CPI CPI-1 CPI-3 Oil Oil-1 Oil-3 Dow Dow-1 Dow-3 Dow Ave (output)
[ 1, 229, 220, 146, 20.0, 21.9, 19.5, 2645, 2652, 2597], [ 2647 ],
[ 2, 235, 226, 155, 19.8, 20.0, 18.3, 2633, 2645, 2585], [ 2637 ],
[ 3, 244, 235, 164, 19.6, 19.8, 18.1, 2627, 2633, 2579], [ 2630 ],
[ 4, 261, 244, 181, 19.6, 19.6, 18.1, 2611, 2627, 2563], [ 2620 ],
[ 5, 276, 261, 196, 19.5, 19.6, 18.0, 2630, 2611, 2582], [ 2638 ],
[ 6, 287, 276, 207, 19.5, 19.5, 18.0, 2637, 2630, 2589], [ 2635 ],
[ 7, 296, 287, 212, 19.3, 19.5, 17.8, 2640, 2637, 2592], [ 2641 ]
);
# Learn the set
my $f = $net->learn_set(\@data,
inc => 0.1,
max => 500,
);
# Print it
print "Forgetfullness: $f%";
This is a snippet from the example script examples/finance.pl, which demonstrates DOW average
prediction for the next month. A more simple set defenition would be as such:
my @data = (
[ 0,1 ], [ 1 ],
[ 1,0 ], [ 0 ]
);
$net->learn_set(\@data);
Same effect as above, but not the same data (obviously).
=item $net->run($input_map_ref);
This method will apply the given array ref at the input layer of the neural network, and
it will return an array ref to the output of the network. run() will now automatically crunch()
a string given as an input (See the crunch() method for info on crunching).
Example Usage:
my $inputs = [ 1,1,0,1 ];
my $outputs = $net->run($inputs);
You can also do this with a string:
my $outputs = $net->run('cloudy - wind is 5 MPH NW');
See also run_uc() and run_set() below.
=item $net->run_uc($input_map_ref);
This method does the same thing as this code:
$net->uncrunch($net->run($input_map_ref));
All that run_uc() does is that it automatically calls uncrunch() on the output, regardless
of whether the input was crunch() -ed or not.
=item $net->run_set($set);
This takes an array ref of the same structure as the learn_set() method, above. It returns
an array ref. Each element in the returned array ref represents the output for the corresponding
element in the dataset passed. Uses run() internally.
=item $net->get_outs($set);
Simple utility function which takes an array ref of the same structure as the learn_set() method,
above. It returns an array ref of the same type as run_set() wherein each element contains an
output value. The output values are the target values specified in the $set passed. Each element
in the returned array ref represents the output value for the corrseponding row in the dataset
passed. (A row is two elements of the dataset together, see learn_set() for dataset structure.)
=item $net->load_set($file,$column,$seperator);
Loads a CSV-like dataset from disk
Returns a data set of the same structure as required by the
learn_set() method. $file is the disk file to load set from.
$column an optional variable specifying the column in the
data set to use as the class attribute. $class defaults to 0.
$seperator is an optional variable specifying the seperator
character between values. $seperator defaults to ',' (a single comma).
NOTE: This does not handle quoted fields, or any other record
seperator other than "\n".
The returned array ref is suitable for passing directly to
learn_set() or get_outs().
=item $net->range();
See CUSTOM ACTIVATION FUNCTIONS for information on several included activation functions.
=item $net->benchmark();
=item $net->benchmarked();
This returns a benchmark info string for the last learn() call.
It is easily printed as a string, as following:
print "Last learn() took ",$net->benchmark(),"\n";
=item $net->verbose($level);
=item $net->verbosity($level);
=item $net->v($level);
=item $net->debug($level)
Note: verbose(), verbosity(), and v() are all functional aliases for debug().
Toggles debugging off if called with $level = 0 or no arguments. There are several levels
of debugging.
NOTE: Debugging verbosity has been toned down somewhat from AI::NeuralNet::BackProp,
but level 4 still prints the same amount of information as you were used to. The other
levels, however, are mostly for advanced use. Not much explanation in the other
levels, but they are included for those of you that feel daring (or just plain bored.)
Level 0 ($level = 0) : Default, no debugging information printed. All printing is
left to calling script.
Level 1 ($level = 1) : Displays the activity between nodes, prints what values were
received and what they were weighted to.
Level 2 ($level = 2) : Just prints info from the learn() loop, in the form of "got: X, wanted Y"
type of information. This is about the third most useful debugging level, after level 12 and
level 4.
Level 3 ($level = 3) : I don't think I included any level 3 debugs in this version.
Level 4 ($level = 4) : This level is the one I use most. It is only used during learning. It
displays the current error (difference between actual outputs and the target outputs you
asked for), as well as the current loop number and the benchmark time for the last learn cycle.
Also printed are the actual outputs and the target outputs below the benchmark times.
Level 12 ($level = 12) : Level 12 prints a dot (period) [.] after each learning loop is
complete. This is useful for letting the user know that stuff is happening, but without
having to display any of the internal variables. I use this in the ex_aln.pl demo,
as well as the ex_agents.pl demo.
Toggles debuging off when called with no arguments.
=item $net->save($filename);
This will save the complete state of the network to disk, including all weights and any
words crunched with crunch() . Also saves the layer size and activations of the network.
NOTE: The only activation type NOT saved is the CODE ref type, which must be set again
after loading.
This uses a simple flat-file text storage format, and therefore the network files should
be fairly portable.
This method will return undef if there was a problem with writing the file. If there is an
error, it will set the internal error message, which you can retrive with the error() method,
below.
If there were no errors, it will return a refrence to $net.
=item $net->load($filename);
This will load from disk any network saved by save() and completly restore the internal
state at the point it was save() was called at.
If the file is of an invalid file type, then load() will
return undef. Use the error() method, below, to print the error message.
If there were no errors, it will return a refrence to $net.
UPDATE: $filename can now be a newline-seperated set of mesh data. This enables you
to do $net->load(join("\n",<DATA>)) and other fun things. I added this mainly
for a demo I'm writing but not qutie done with yet. So, Cheers!
=item $net->activation($layer,$type);
This sets the activation type for layer C<$layer>.
C<$type> can be one of four values:
linear ( simply use sum of inputs as output )
sigmoid [ sigmoid_1 ] ( only positive sigmoid )
sigmoid_2 ( positive / 0 /negative sigmoid )
\&code_ref;
"sigmoid_1" is an alias for "sigmoid".
The code ref option allows you to have a custom activation function for that layer.
The code ref is called with this syntax:
$output = &$code_ref($sum_of_inputs, $self);
The code ref is expected to return a value to be used as the output of the node.
The code ref also has access to all the data of that node through the second argument,
a blessed hash refrence to that node.
See CUSTOM ACTIVATION FUNCTIONS for information on several included activation functions
other than the ones listed above.
The activation type for each layer is preserved across load/save calls.
EXCEPTION: Due to the constraints of Perl, I cannot load/save the actual subs that the code
ref option points to. Therefore, you must re-apply any code ref activation types after a
load() call.
=item $net->node_activation($layer,$node,$type);
This sets the activation function for a specific node in a layer. The same notes apply
here as to the activation() method above.
=item $net->threshold($layer,$value);
This sets the activation threshold for a specific layer. The threshold only is used
when activation is set to "sigmoid", "sigmoid_1", or "sigmoid_2".
=item $net->node_threshold($layer,$node,$value);
This sets the activation threshold for a specific node in a layer. The threshold only is used
when activation is set to "sigmoid", "sigmoid_1", or "sigmoid_2".
=item $net->join_cols($array_ref,$row_length_in_elements,$high_state_character,$low_state_character);
This is more of a utility function than any real necessary function of the package.
Instead of joining all the elements of the array together in one long string, like join() ,
it prints the elements of $array_ref to STDIO, adding a newline (\n) after every $row_length_in_elements
number of elements has passed. Additionally, if you include a $high_state_character and a $low_state_character,
it will print the $high_state_character (can be more than one character) for every element that
has a true value, and the $low_state_character for every element that has a false value.
If you do not supply a $high_state_character, or the $high_state_character is a null or empty or
undefined string, it join_cols() will just print the numerical value of each element seperated
by a null character (\0). join_cols() defaults to the latter behaviour.
=item $net->extend(\@array_of_hashes);
This allows you to re-apply any activations and thresholds with the same array ref which
you created a network with. This is useful for re-applying code ref activations after a load()
call without having to type the code ref twice.
You can also specify the extension in a simple array ref like this:
$net->extend([2,3,1]);
Which will simply add more nodes if needed to set the number of nodes in each layer to their
respective elements. This works just like the respective new() constructor, above.
NOTE: Your net will probably require re-training after adding nodes.
=item $net->extend_layer($layer,\%hash);
With this you can modify only one layer with its specifications in a hash refrence. This hash
refrence uses the same keys as for the last new() constructor form, above.
You can also specify just the number of nodes for the layer in this form:
$net->extend_layer(0,5);
Which will set the number of nodes in layer 0 to 5 nodes. This is the same as calling:
$net->add_nodes(0,5);
Which does the exact same thing. See add_nodes() below.
NOTE: Your net will probably require re-training after adding nodes.
=item $net->add_nodes($layer,$total_nodes);
This method was created mainly to service the extend*() group of functions, but it
can also be called independently. This will add nodes as needed to layer C<$layer> to
make the nodes in layer equal to $total_nodes.
NOTE: Your net will probably require re-training after adding nodes.
=item $net->p($a,$b);
Returns a floating point number which represents $a as a percentage of $b.
=item $net->intr($float);
Rounds a floating-point number rounded to an integer using sprintf() and int() , Provides
better rounding than just calling int() on the float. Also used very heavily internally.
=item $net->high($array_ref);
Returns the index of the element in array REF passed with the highest comparative value.
=item $net->low($array_ref);
Returns the index of the element in array REF passed with the lowest comparative value.
=item $net->pdiff($array_ref_A, $array_ref_B);
This function is used VERY heavily internally to calculate the difference in percent
between elements of the two array refs passed. It returns a %.20f (sprintf-format)
percent sting.
=item $net->show();
This will dump a simple listing of all the weights of all the connections of every neuron
in the network to STDIO.
=item $net->crunch($string);
This splits a string passed with /[\s\t]/ into an array ref containing unique indexes
to the words. The words are stored in an intenal array and preserved across load() and save()
calls. This is designed to be used to generate unique maps sutible for passing to learn() and
run() directly. It returns an array ref.
The words are not duplicated internally. For example:
$net->crunch("How are you?");
Will probably return an array ref containing 1,2,3. A subsequent call of:
$net->crunch("How is Jane?");
Will probably return an array ref containing 1,4,5. Notice, the first element stayed
the same. That is because it already stored the word "How". So, each word is stored
only once internally and the returned array ref reflects that.
=item $net->uncrunch($array_ref);
Uncrunches a map (array ref) into an scalar string of words seperated by ' ' and returns the
string. This is ment to be used as a counterpart to the crunch() method, above, possibly to
uncrunch() the output of a run() call. Consider the below code (also in ./examples/ex1.pl):
use AI::NeuralNet::Mesh;
my $net = AI::NeuralNet::Mesh->new(2,3);
for (0..3) {
$net->learn_set([
$net->crunch("I love chips."), $net->crunch("That's Junk Food!")),
$net->crunch("I love apples."), $net->crunch("Good, Healthy Food.")),
$net->crunch("I love pop."), $net->crunch("That's Junk Food!")),
$net->crunch("I love oranges."),$net->crunch("Good, Healthy Food."))
]);
}
print $net->run_uc("I love corn.")),"\n";
On my system, this responds with, "Good, Healthy Food." If you try to run crunch() with
"I love pop.", though, you will probably get "Food! apples. apples." (At least it returns
that on my system.) As you can see, the associations are not yet perfect, but it can make
for some interesting demos!
=item $net->crunched($word);
This will return undef if the word is not in the internal crunch list, or it will return the
index of the word if it exists in the crunch list.
If the word is not in the list, it will set the internal error value with a text message
that you can retrive with the error() method, below.
=item $net->word($word);
A function alias for crunched().
=item $net->col_width($width);
This is useful for formating the debugging output of Level 4 if you are learning simple
bitmaps. This will set the debugger to automatically insert a line break after that many
elements in the map output when dumping the currently run map during a learn loop.
It will return the current width when called with a 0 or undef value.
The column width is preserved across load() and save() calls.
=item $net->random($rand);
This will set the randomness factor from the network. Default is 0. When called
with no arguments, or an undef value, it will return current randomness value. When
called with a 0 value, it will disable randomness in the network. The randomness factor
is preserved across load() and save() calls.
=item $net->const($const);
This sets the run const. for the network. The run const. is a value that is added
to every input line when a set of inputs are run() or learn() -ed, to prevent the
network from hanging on a 0 value. When called with no arguments, it returns the current
const. value. It defaults to 0.0001 on a newly-created network. The run const. value
is preserved across load() and save() calls.
=item $net->error();
Returns the last error message which occured in the mesh, or undef if no errors have
occured.
=item $net->load_pcx($filename);
NOTE: To use this function, you must have PCX::Loader installed. If you do not have
PCX::Loader installed, it will return undef and store an error for you to retrive with
the error() method, below.
This is a treat... this routine will load a PCX-format file (yah, I know ... ancient
format ... but it is the only one I could find specs for to write it in Perl. If
anyone can get specs for any other formats, or could write a loader for them, I
would be very grateful!) Anyways, a PCX-format file that is exactly 320x200 with 8 bits
per pixel, with pure Perl. It returns a blessed refrence to a PCX::Loader object, which
supports the following routinges/members. See example files ex_pcx.pl and ex_pcxl.pl in
the ./examples/ directory.
See C<perldoc PCX::Loader> for information on the methods of the object returned.
You can download PCX::Loader from
http://www.josiah.countystart.com/modules/get.pl?pcx-loader:mpod
=head1 CUSTOM ACTIVATION FUNCTIONS
Included in this package are four custom activation functions meant to be used
as a guide to create your own, as well as to be useful to you in normal use of the
module. There is only one function exported by default into your namespace, which
is the range() functions. These are not meant to be used as methods, but as functions.
These functions return code refs to a Perl closure which does the actual work when
the time comes.
=item range(0..X);
=item range(@range);
=item range(A,B,C);
range() returns a closure limiting the output
of that node to a specified set of values.
Good for use in output layers.
Usage example:
$net->activation(4,range(0..5));
or (in the new() hash constructor form):
..
{
nodes => 1,
activation => range 5..2
}
..
You can also pass an array containing the range
values (not array ref), or you can pass a comma-
seperated list of values as parameters:
$net->activation(4,range(@numbers));
$net->activation(4,range(6,15,26,106,28,3));
Note: when using a range() activatior, train the
net TWICE on the data set, because the first time
the range() function searches for the top value in
the inputs, and therefore, results could flucuate.
The second learning cycle guarantees more accuracy.
The actual code that implements the range closure is
a bit convulted, so I will expand on it here as a simple
tutorial for custom activation functions.
= line 1 = sub {
= line 2 = my @values = ( 6..10 );
= line 3 = my $sum = shift;
= line 4 = my $self = shift;
= line 5 = $self->{top_value}=$sum if($sum>$self->{top_value});
= line 6 = my $index = intr($sum/$self->{top_value}*$#values);
= line 7 = return $values[$index];
= line 8 = }
Now, the actual function fits in one line of code, but I expanded it a bit
here. Line 1 creates our array of allowed output values. Lines two and
three grab our parameters off the stack which allow us access to the
internals of this node. Line 5 checks to see if the sum output of this
node is higher than any previously encountered, and, if so, it sets
the marker higher. This also shows that you can use the $self refrence
to maintain information across activations. This technique is also used
in the ramp() activator. Line 6 computes the index into the allowed
values array by first scaling the $sum to be between 0 and 1 and then
expanding it to fit smoothly inside the number of elements in the array. Then
we simply round to an integer and pluck that index from the array and
use it as the output value for that node.
See? It's not that hard! Using custom activation functions, you could do
just about anything with the node that you want to, since you have
access to the node just as if you were a blessed member of that node's object.
=item ramp($r);
ramp() preforms smooth ramp activation between 0 and 1 if $r is 1,
or between -1 and 1 if $r is 2. $r defaults to 1.
You can get this into your namespace with the ':acts' export
tag as so:
use AI::NeuralNet::Mesh ':acts';
Note: when using a ramp() activatior, train the
net at least TWICE on the data set, because the first
time the ramp() function searches for the top value in
the inputs, and therefore, results could flucuate.
The second learning cycle guarantees more accuracy.
No code to show here, as it is almost exactly the same as range().
=item and_gate($threshold);
Self explanitory, pretty much. This turns the node into a basic AND gate.
$threshold is used to decide if an input is true or false (1 or 0). If
an input is below $threshold, it is false. $threshold defaults to 0.5.
You can get this into your namespace with the ':acts' export
tag as so:
use AI::NeuralNet::Mesh ':acts';
Let's look at the code real quick, as it shows how to get at the indivudal
input connections:
= line 1 = sub {
= line 2 = my $sum = shift;
= line 3 = my $self = shift;
= line 4 = my $threshold = 0.50;
= line 5 = for my $x (0..$self->{_inputs_size}-1) {
= line 6 = return 0.000001 if(!$self->{_inputs}->[$x]->{value}<$threshold)
= line 7 = }
= line 8 = return $sum/$self->{_inputs_size};
= line 9 = }
Line 2 and 3 pulls in our sum and self refrence. Line 5 opens a loop to go over
all the input lines into this node. Line 6 looks at each input line's value
and comparse it to the threshold. If the value of that line is below threshold, then
we return 0.000001 to signify a 0 value. (We don't return a 0 value so that the network
doen't get hung trying to multiply a 0 by a huge weight during training [it just will
keep getting a 0 as the product, and it will never learn]). Line 8 returns the mean
value of all the inputs if all inputs were above threshold.
Very simple, eh? :)
=item or_gate($threshold)
Self explanitory. Turns the node into a basic OR gate, $threshold is used same as above.
You can get this into your namespace with the ':acts' export
tag as so:
use AI::NeuralNet::Mesh ':acts';
=head1 VARIABLES
=item $AI::NeuralNet::Mesh::Connector
This is an option is step up from average use of this module. This variable
should hold the fully qualified name of the function used to make the actual connections
between the nodes in the network. This contains '_c' by default, but if you use
this variable, be sure to add the fully qualified name of the method. For example,
in the ALN example, I use a connector in the main package called tree() instead of
the default connector. Before I call the new() constructor, I use this line of code:
$AI::NeuralNet::Mesh::Connector = 'main::tree'
The tree() function is called as a blessed method when it is used internally, providing
access to the bless refrence in the first argument. See notes on CUSTOM NETWORK CONNECTORS,
below, for more information on creating your own custom connector.
=item $AI::NeuralNet::Mesh::DEBUG
This variable controls the verbosity level. It will not hurt anything to set this
directly, yet most people find it easier to set it using the debug() method, or
any of its aliases.
=head1 CUSTOM NETWORK CONNECTORS
Creating custom network connectors is step up from average use of this module.
However, it can be very useful in creating other styles of neural networks, other
than the default fully-connected feed-foward network.
You create a custom connector by setting the variable $AI::NeuralNet::Mesh::Connector
to the fully qualified name of the function used to make the actual connections
between the nodes in the network. This variable contains '_c' by default, but if you use
this variable, be sure to add the fully qualified name of the method. For example,
in the ALN example, I use a connector in the main package called tree() instead of
the default connector. Before I call the new() constructor, I use this line of code:
$AI::NeuralNet::Mesh::Connector = 'main::tree'
The tree() function is called as a blessed method when it is used internally, providing
access to the bless refrence in the first argument.
Example connector:
sub connect_three {
my $self = shift;
my $r1a = shift;
my $r1b = shift;
my $r2a = shift;
my $r2b = shift;
my $mesh = $self->{mesh};
for my $y (0..($r1b-$r1a)-1) {
$mesh->[$y+$r1a]->add_output_node($mesh->[$y+$r2a-1]) if($y>0);
$mesh->[$y+$r1a]->add_output_node($mesh->[$y+$r2a]) if($y<($r2b-$r2a));
$mesh->[$y+$r1a]->add_output_node($mesh->[$y+$r2a+1]) if($y<($r2b-$r2a));
}
}
This is a very simple example. It feeds the outputs of every node in the first layer
to the node directly above it, as well as the nodes on either side of the node directly
above it, checking for range sides, of course.
The network is stored internally as one long array of node objects. The goal here
is to connect one range of nodes in that array to another range of nodes. The calling
function has already calculated the indices into the array, and it passed it to you
as the four arguments after the $self refrence. The first two arguments we will call
$r1a and $r1b. These define the start and end indices of the first range, or "layer." Likewise,
the next two arguemnts, $r2a and $r2b, define the start and end indices of the second
layer. We also grab a refrence to the mesh array so we dont have to type the $self
refrence over and over.
The loop that folows the arguments in the above example is very simple. It opens
a for() loop over the range of numbers, calculating the size instead of just going
$r1a..$r1b because we use the loop index with the next layer up as well.
$y + $r1a give the index into the mesh array of the current node to connect the output FROM.
We need to connect this nodes output lines to the next layers input nodes. We do this
with a simple method of the outputing node (the node at $y+$r1a), called add_output_node().
add_output_node() takes one simple arguemnt: A blessed refrence to a node that it is supposed
to output its final value TO. We get this blessed refrence with more simple addition.
$y + $r2a gives us the node directly above the first node (supposedly...I'll get to the "supposedly"
part in a minute.) By adding or subtracting from this number we get the neighbor nodes.
In the above example you can see we check the $y index to see that we havn't come close to
any of the edges of the range.
Using $y+$r2a we get the index of the node to pass to add_output_node() on the first node at
$y+B<$r1a>.
And that's all there is to it!
For the fun of it, we'll take a quick look at the default connector.
Below is the actual default connector code, albeit a bit cleaned up, as well as
line numbers added.
= line 1 = sub _c {
= line 2 = my $self = shift;
= line 3 = my $r1a = shift;
= line 4 = my $r1b = shift;
= line 5 = my $r2a = shift;
= line 6 = my $r2b = shift;
= line 7 = my $mesh = $self->{mesh};
= line 8 = for my $y ($r1a..$r1b-1) {
= line 9 = for my $z ($r2a..$r2b-1) {
= line 10 = $mesh->[$y]->add_output_node($mesh->[$z]);
= line 11 = }
= line 12 = }
= line 12 = }
Its that easy! The simplest connector (well almost anyways). It just connects each
node in the first layer defined by ($r1a..$r1b) to every node in the second layer as
defined by ($r2a..$r2b).
Those of you that are still reading, if you do come up with any new connection functions,
PLEASE SEND THEM TO ME. I would love to see what others are doing, as well as get new
network ideas. I will probably include any connectors you send over in future releases (with
propoer credit and permission, of course).
Anyways, happy coding!
=head1 WHAT CAN IT DO?
Rodin Porrata asked on the ai-neuralnet-backprop malining list,
"What can they [Neural Networks] do?". In regards to that questioin,
consider the following:
Neural Nets are formed by simulated neurons connected together much the same
way the brain's neurons are, neural networks are able to associate and
generalize without rules. They have solved problems in pattern recognition,
robotics, speech processing, financial predicting and signal processing, to
name a few.
One of the first impressive neural networks was NetTalk, which read in ASCII
text and correctly pronounced the words (producing phonemes which drove a
speech chip), even those it had never seen before. Designed by John Hopkins
biophysicist Terry Sejnowski and Charles Rosenberg of Princeton in 1986,
this application made the Backprogagation training algorithm famous. Using
the same paradigm, a neural network has been trained to classify sonar
returns from an undersea mine and rock. This classifier, designed by
Sejnowski and R. Paul Gorman, performed better than a nearest-neighbor
classifier.
The kinds of problems best solved by neural networks are those that people
are good at such as association, evaluation and pattern recognition.
Problems that are difficult to compute and do not require perfect answers,
just very good answers, are also best done with neural networks. A quick,
very good response is often more desirable than a more accurate answer which
takes longer to compute. This is especially true in robotics or industrial
controller applications. Predictions of behavior and general analysis of
data are also affairs for neural networks. In the financial arena, consumer
loan analysis and financial forecasting make good applications. New network
designers are working on weather forecasts by neural networks (Myself
included). Currently, doctors are developing medical neural networks as an
aid in diagnosis. Attorneys and insurance companies are also working on
neural networks to help estimate the value of claims.
Neural networks are poor at precise calculations and serial processing. They
are also unable to predict or recognize anything that does not inherently
contain some sort of pattern. For example, they cannot predict the lottery,
since this is a random process. It is unlikely that a neural network could
be built which has the capacity to think as well as a person does for two
reasons. Neural networks are terrible at deduction, or logical thinking and
the human brain is just too complex to completely simulate. Also, some
problems are too difficult for present technology. Real vision, for
example, is a long way off.
In short, Neural Networks are poor at precise calculations, but good at
association, evaluation, and pattern recognition.
=head1 EXAMPLES
Included are several example files in the "examples" directory from the
distribution ZIP file. Each of the examples includes a short explanation
at the top of the file. Each of these are ment to demonstrate simple, yet
practical (for the most part :-) uses of this module.
=head1 OTHER INCLUDED PACKAGES
These packages are not designed to be called directly, they are for internal use. They are
listed here simply for your refrence.
=item AI::NeuralNet::Mesh::node
This is the worker package of the mesh. It implements all the individual nodes of the mesh.
It might be good to look at the source for this package (in the Mesh.pm file) if you
plan to do a lot of or extensive custom node activation types.
=item AI::NeuralNet::Mesh::cap
This is applied to the input layer of the mesh to prevent the mesh from trying to recursivly
adjust weights out throug the inputs.
=item AI::NeuralNet::Mesh::output
This is simply a data collector package clamped onto the output layer to record the data
as it comes out of the mesh.
=head1 BUGS
This is a beta release of C<AI::NeuralNet::Mesh>, and that holding true, I am sure
there are probably bugs in here which I just have not found yet. If you find bugs in this module, I would
appreciate it greatly if you could report them to me at F<E<lt>jdb@wcoil.comE<gt>>,
or, even better, try to patch them yourself and figure out why the bug is being buggy, and
send me the patched code, again at F<E<lt>jdb@wcoil.comE<gt>>.
=head1 AUTHOR
Josiah Bryan F<E<lt>jdb@wcoil.comE<gt>>
Copyright (c) 2000 Josiah Bryan. All rights reserved. This program is free software;
you can redistribute it and/or modify it under the same terms as Perl itself.
The C<AI::NeuralNet::Mesh> and related modules are free software. THEY COME WITHOUT WARRANTY OF ANY KIND.
$Id: AI::NeuralNet::Mesh.pm, v0.44 2000/15/09 03:29:08 josiah Exp $
=head1 THANKS
Below are a list of the people that have contributed in some way to this module (no particular order):
Rodin Porrata, rodin@ursa.llnl.gov
Randal L. Schwartz, merlyn@stonehedge.com
Michiel de Roo, michiel@geo.uu.nl
Thanks to Randal and Michiel for spoting some documentation and makefile bugs in the last release.
Thanks to Rodin for continual suggetions and questions about the module and more.
=head1 DOWNLOAD
You can always download the latest copy of AI::NeuralNet::Mesh
from http://www.josiah.countystart.com/modules/get.pl?mesh:pod
=head1 MAILING LIST
A mailing list has been setup for AI::NeuralNet::Mesh and AI::NeuralNet::BackProp.
The list is for discussion of AI and neural net related topics as they pertain to
AI::NeuralNet::BackProp and AI::NeuralNet::mesh. I will also announce in the group
each time a new release of AI::NeuralNet::Mesh is available.
The list address is at:
ai-neuralnet-backprop@egroups.com
To subscribe, send a blank email:
ai-neuralnet-backprop-subscribe@egroups.com
=cut
Greetings Perlfolk,
** What is this?
AI::NeuralNet::Mesh is an optimized, accurate neural network Mesh.
It was designed with accruacy and speed in mind.
This network model is very flexable. It will allow for clasic binary
operation or any range of integer or floating-point inputs you care
to provide. With this you can change activation types on a per node or
per layer basis (you can even include your own anonymous subs as
activation types). You can add sigmoid transfer functions and control
the threshold. You can learn data sets in batch, and load CSV data
set files. You can do almost anything you need to with this module.
This code is deigned to be flexable. Any new ideas for this module?
Contact Josiah Bryan at <jdb@wcoil.com>
This module is designed to also be a customizable, extensable
neural network simulation toolkit. Through a combination of setting
the $Connection variable and using custom activation functions, as
well as basic package inheritance, you can simulate many different
types of neural network structures with very little new code written
by you. (See ex_aln.pl)
As always, included is a cleaned, CSS-ed, HTML-format of the POD docs.
** What's new?
>From the POD:
This is version 0.44, an bug fix for the third release of the module.
This fixed a compatibilty issue that 0.43 had with Perl 5.3.3
With this version I have gone through and tuned up many area
of this module, including the descent algorithim in learn(),
as well as four custom activation functions, and several export
tag sets. With this release, I have also included a few
new and more practical example scripts. (See ex_wine.pl) This release
also includes a simple example of an ALN (Adaptive Logic Network) made
with this module. See ex_aln.pl. Also in this release is support for
loading data sets from simple CSV-like files. See the load_set() method
for details. This version also fixes a big bug that I never knew about
until writing some demos for this version - that is, when trying to use
more than one output node, the mesh would freeze in learning. But, that
is fixed now, and you can have as many outputs as you want (how does 3
inputs and 50 outputs sound? :-) Also in this release is output range
limiting via the range() activation function.
** What do you think?
Now I know you people are out there that are using the module...
I can hear the fists hitting the keyboards in frustration. :-) Relieve
some of that frustration by e-mailing me and letting me know what
you think of the module and any suggestions you got.
Use it, let me know what you all think. This is just a
groud-up write of a neural network, no code stolen or
anything else. Don't expect a classicist view of nerual
networking here. I simply wrote from operating theory,
not math theory. Any die-hard neural networking gurus out
there? Let me know how far off I am with
this code! :-)
Regards,
~ Josiah Bryan, <jdb@wcoil.com>
Latest Version:
http://www.josiah.countystart.com/modules/get.pl?mesh:README
examples/addnet_data.txt view on Meta::CPAN
layers inc top forgetfulness time %diff1 %diff2 %diff3
%diff4
1 0.025 1 0 0 wallclock secs ( 0.06 usr + 0.00 sys = 0.06 CPU) 0.000000 0.000000 0.000000 0.000000
1 0.025 2 0 0 wallclock secs ( 0.06 usr + 0.00 sys = 0.06 CPU) 0.000000 0.000000 0.000000 0.000000
1 0.025 3 0 0 wallclock secs ( 0.11 usr + 0.00 sys = 0.11 CPU) 0.000000 0.000000 0.000000 0.000000
1 0.025 4 0 0 wallclock secs ( 0.17 usr + 0.00 sys = 0.17 CPU) 0.000000 0.000000 0.000000 0.000000
1 0.050 1 0 0 wallclock secs ( 0.00 usr + 0.00 sys = 0.00 CPU) 0.000000 0.000000 0.000000 0.000000
1 0.050 2 0 0 wallclock secs ( 0.06 usr + 0.00 sys = 0.06 CPU) 0.000000 0.000000 0.000000 0.000000
1 0.050 3 0 0 wallclock secs ( 0.11 usr + 0.00 sys = 0.11 CPU) 0.000000 0.000000 0.000000 0.000000
1 0.050 4 0 0 wallclock secs ( 0.16 usr + 0.00 sys = 0.16 CPU) 0.000000 0.000000 0.000000 0.000000
1 0.075 1 0 0 wallclock secs ( 0.00 usr + 0.00 sys = 0.00 CPU) 0.000000 0.000000 0.000000 0.000000
1 0.075 2 0 0 wallclock secs ( 0.05 usr + 0.00 sys = 0.05 CPU) 0.000000 0.000000 0.000000 0.000000
examples/ex_add.pl view on Meta::CPAN
=begin
File: examples/ex_add.pl
Author: Josiah Bryan, <jdb@wcoil.com>
Desc:
This demonstrates the ability of a neural net to generalize
and predict what the correct result is for inputs that it has
never seen before.
This teaches a network to add 11 sets of numbers, then it asks
the user for two numbers to add and it displays the results of
the user's input.
=cut
use AI::neuralNet::Mesh;
my $addition = new AI::NeuralNet::Mesh(2,2,1);
if(!$addition->load('add.mesh')) {
$addition->learn_set([
[ 1, 1 ], [ 2 ] ,
[ 1, 2 ], [ 3 ],
[ 2, 2 ], [ 4 ],
[ 20, 20 ], [ 40 ],
[ 50, 50 ], [ 100 ],
[ 60, 40 ], [ 100 ],
[ 100, 100 ], [ 200 ],
[ 150, 150 ], [ 300 ],
[ 500, 500 ], [ 1000 ],
[ 10, 10 ], [ 20 ],
[ 15, 15 ], [ 30 ],
[ 12, 8 ], [ 20 ],
]);
$addition->save('add.mesh');
}
print "Enter first number to add : "; chomp(my $a = <>);
print "Enter second number to add : "; chomp(my $b = <>);
print "Result: ",$addition->run([$a,$b])->[0],"\n";
examples/ex_add2.pl view on Meta::CPAN
=begin
File: examples/ex_add2.pl
Author: Rodin Porrata, <rodin@ursa.llnl.gov>
Desc:
This script runs a test of the networks ability to add
and remember data sets, as well as testing the optimum "inc" to
learn and the optimum number of layers for a network.
=cut
use AI::NeuralNet::Mesh;
use Benchmark;
use English;
my $ofile = "addnet_data.txt";
open( OUTFP, ">$ofile" ) or die "Could not open output file\n";
my ( $layers, $inputs, $outputs, $top, $inc, $top, $runtime,
$forgetfulness );
my @answers;
my @predictions;
my @percent_diff;
$inputs = 3;
$outputs = 1;
my ($maxinc,$maxtop,$incstep);
select OUTFP; $OUTPUT_AUTOFLUSH = 1; select STDOUT;
print OUTFP "layers inc top forgetfulness time \%diff1 \%diff2 \%diff3
\%diff4\n\n";
for( $layers = 1; $layers <= 3; $layers++ ){
if( $layers <= 2 ){
$incstep = 0.025;
}
else{
$incstep = 0.05;
}
for( $inc=0.025; $inc <= 0.4; $inc += $incstep ){
if( $inc > .3 ){
$maxtop = 3;
}
else{
$maxtop = 4;
}
for( $top=1; $top <=$maxtop; $top++ ){
addnet();
printf OUTFP "%d %.3f %d %g %s %f %f %f %f\n",
$layers, $inc, $top, $forgetfulness, timestr($runtime),
$percent_diff[0],
$percent_diff[1], $percent_diff[2], $percent_diff[3];
print "layers inc top forgetfulness time \%diff1 \%diff2 \%diff3
\%diff4\n";
printf "%d %.3f %d %g %s %f %f %f %f\n",
$layers, $inc, $top, $forgetfulness, timestr($runtime),
$percent_diff[0],
$percent_diff[1], $percent_diff[2], $percent_diff[3];
}
}
}
#....................................................
sub addnet
{
print "\nCreate a new net with $layers layers, 3 inputs, and 1 output\n";
my $net = AI::NeuralNet::Mesh->new($layers,3,1);
# Disable debugging
$net->debug(0);
my @data = (
[ 2633, 2665, 2685], [ 2633 + 2665 + 2685 ],
[ 2623, 2645, 2585], [ 2623 + 2645 + 2585 ],
[ 2627, 2633, 2579], [ 2627 + 2633 + 2579 ],
[ 2611, 2627, 2563], [ 2611 + 2627 + 2563 ],
[ 2640, 2637, 2592], [ 2640 + 2637 + 2592 ]
);
print "Learning started, will cycle $top times with inc = $inc\n";
# Make it learn the whole dataset $top times
my @list;
my $t1=new Benchmark;
for my $a (1..$top)
{
print "Outer Loop: $a : ";
$forgetfulness = $net->learn_set( \@data,
inc => $inc,
max => 500,
error => -1);
print "Forgetfulness: $forgetfulness %\n";
}
my $t2=new Benchmark;
$runtime = timediff($t2,$t1);
print "run took ",timestr($runtime),"\n";
my @input = ( [ 2222, 3333, 3200 ],
[ 1111, 1222, 3211 ],
[ 2345, 2543, 3000 ],
[ 2654, 2234, 2534 ] );
test_net( $net, @input );
}
#.....................................................................
sub test_net {
my @set;
my $fb;
my $net = shift;
my @data = @_;
undef @percent_diff; #@answers; undef @predictions;
for( $i=0; defined( $data[$i] ); $i++ ){
@set = @{ $data[$i] };
$fb = $net->run(\@set)->[0];
# Print output
print "Test Factors: (",join(',',@set),")\n";
$answer = eval( join( '+',@set ));
push @percent_diff, 100.0 * abs( $answer - $fb )/ $answer;
print "Prediction : $fb answer: $answer\n";
}
}
examples/ex_aln.pl view on Meta::CPAN
=begin
File: examples/ex_aln.pl
Author: Josiah Bryan, jdb@wcoil.com
Desc:
This is a simple example of a _basic_ ALN implementation in
under 210 lines of code. In this demo we make use of the
custom node connector as described in the POD. We also
insert our own method over the node's internal adjust_weight()
method to make ALN learning a bit easire. This demo also adds
a temporary method to the network to print the logical type of
each node, called print_aln();
print_aln() prints simple diagram of the
network similar to this (this is for a $net=Tree(8,1) with
$net->learn([1,1,0,1,0,1,1,1],[0]), and each line represents
a layer):
L R L L L L L L
OR OR OR OR
OR OR
AND
All the standard methods that work on AI::NeuralNet::Mesh work
on the object returned by Tree(). load() and save() will correctly
preserve the gate structure and types of your network. learn_set()
and everything else works pretty much as expected. Only thing
that is useless is the crunch() method, as this only takes binary
inputs. But...for those of you who couldnt live without integers
in your network...I'm going to create a small package in the next
week, AI::NeuralNet::ALNTree, from this code. It will which includes
a integer-vectorizer (convert your integers into bit vectors), a bit
vector class to play with, as well as support for concating and
learning bit vectors. But, for now, enjoy this!
This file contains just a simple, functional, ALN implementation.
Enjoy!
=cut
# Import all the little functions.
use AI::NeuralNet::Mesh ':all';
# Create a new ALN tree with 2 leaves and 1 root node.
# Note: Our ALN trees can have more than one root node! Yippe! :-)
# Just a little benefit of deriving our ALNs from
# AI::NeuralNet::Mesh.
#
my $net = Tree(8,1);
# Use our nifty dot verbosity.
$net->v(12);
# Learn a pattern and print stats.
if(!$net->load('aln.mesh')) {
print "Learning";
print "Done!\nLearning took ",$net->learn([1,1,0,1,0,1,1,1],[0]),"\n";
$net->save('aln.mesh');
}
# Print logic gate types
$net->print_aln();
# Test it out
print "\nPattern: [1,1,0,1,0,1,1,1]".
"\nResult: ",$net->run([1,1,1,1,1,1,1,1])->[0],"\n";
######################################################################
#-################ ALN Implementation Code ########################-#
######################################################################
# Build a basic ALN tree network (_very_ basic, only implements
# the node types, and only two learning benefits from ALN theory are
# realized.) Also adds a method to the neural network gates, print_aln().
sub Tree {
# Grab our leaves and roots
my $leaves = shift;
my $roots = shift || $leaves;
# Replace the load function with a new one to preserve the
# load activations. We have to add this up here because next
# thing we do is check if they passed a file name as $leaves,
# and we need to have our new load sub already in place before
# we try to load anything in $leaves.
*{'AI::NeuralNet::Mesh::load'} = sub {
my $self = shift;
my $file = shift;
my $load_flag = shift;
if(!(-f $file)) {
$self->{error} = "File \"$file\" does not exist.";
return undef;
}
open(FILE,"$file");
my @lines=<FILE>;
close(FILE);
my %db;
for my $line (@lines) {
chomp($line);
my ($a,$b) = split /=/, $line;
$db{$a}=$b;
}
if(!$db{"header"}) {
$self->{error} = "Invalid format.";
return undef;
}
return $self->load_old($file) if($self->version($db{"header"})<0.21);
if($load_flag) {
undef $self;
$self = Tree($db{inputs},$db{outputs});
} else {
$self->{inputs} = $db{inputs};
$self->{nodes} = $db{nodes};
$self->{outputs} = $db{outputs};
$self->{layers} = [split(',',$db{layers})];
$self->{total_layers} = $db{total_layers};
$self->{total_nodes} = $db{total_nodes};
}
# Load variables
$self->{random} = $db{"rand"};
$self->{const} = $db{"const"};
$self->{col_width} = $db{"cw"};
$self->{rA} = $db{"rA"};
$self->{rB} = $db{"rB"};
$self->{rS} = $db{"rS"};
$self->{rRef} = [split /\,/, $db{"rRef"}];
$self->{_crunched}->{_length} = $db{"crunch"};
for my $a (0..$self->{_crunched}->{_length}-1) {
$self->{_crunched}->{list}->[$a] = $db{"c$a"};
}
$self->_init();
my $n = 0;
for my $x (0..$self->{total_layers}) {
for my $y (0..$self->{layers}->[$x]-1) {
my @l = split /\,/, $db{"n$n"};
for my $z (0..$self->{layers}->[$x-1]-1) {
$self->{mesh}->[$n]->{_inputs}->[$z]->{weight} = $l[$z];
}
my $z = $self->{layers}->[$x-1];
$self->{mesh}->[$n]->{activation} = $l[$z];
$self->{mesh}->[$n]->{threshold} = $l[$z+1];
$self->{mesh}->[$n]->{mean} = $l[$z+2];
$n++;
}
}
$self->extend($self->{_original_specs});
return $self;
};
# If $leavesis a string, then it will be numerically equal to 0, so
# try to load it as a network file.
if($leaves == 0) {
# We use a "1" flag as the second argument to indicate that we
# want load() to call the new constructor to make a network the
# same size as in the file and return a refrence to the network,
# instead of just creating the network from pre-exisiting refrence
my $self = AI::NeuralNet::Mesh->new(1,1);
return $self->load($leaves,1);
}
# Initalize our counter and our specs ref
my $specs = [];
my $level = 0;
# Create our custom node activation
my $act = sub {
shift; my $self = shift;
my $b1 = intr($self->{_inputs}->[0]->{weight});
my $b2 = intr($self->{_inputs}->[1]->{weight});
my $x1 = intr($self->{_inputs}->[0]->{input});
my $x2 = intr($self->{_inputs}->[1]->{input});
# node type: $b1 $b2
# OR : 1 1
# AND : 0 0
# L : 1 0
# R : 0 1
# This is made possible by this little four-way
# forumla is from the ATREE 2.7 demo by
# M. Thomas, <monroe@cs.UAlberta.CA>
$self->{_last_output} = ($b1+1)*$x1 + ($b2+1)*$x2 >= 2 ? 1 : 0;
# We store the last output to use in our custom
# weight adjustment function, below.
return $self->{_last_output};
};
# Adjust the leaves so it divides into a number divisible
# evenly by two.
__LEAF_IT:
$leaves++ if($leaves%2 && $leaves!=1);
$leaves++,goto __LEAF_IT if(($leaves/2)%2);
# Create a layer spec array with every layer having half
# the number of nodes of the layer before it
while($leaves!=$roots) {
$specs->[$level++]={ nodes=>$leaves, activation=>$act };
$leaves/=2;
$leaves++ if($leaves%2 && $leaves!=$roots);
}
$specs->[$level++]={ nodes=>$roots, activation=>$act };
# Add a method to the net to print out the node types
*{'AI::NeuralNet::Mesh::print_aln'} = sub {
my $self=shift;
my ($c,$l)=(0,0);
for(0..$self->{total_nodes}-1) {
my $b1 = intr($self->{mesh}->[$_]->{_inputs}->[0]->{weight});
my $b2 = intr($self->{mesh}->[$_]->{_inputs}->[1]->{weight});
print "OR " if( $b1 && $b2);
print "AND " if(!$b1 && !$b2);
print "L " if( $b1 && !$b2);
print "R " if(!$b1 && $b2);
$c=0,$l++,print "\n" if++$c>=$self->{layers}->[$l];
}
};
# Add a custom node weight adjuster to learn faster
*{'AI::NeuralNet::Mesh::node::adjust_weight'} = sub {
my ($self,$inc,$taget) = @_;
my $f;
my $b1 = intr($self->{mesh}->[$_]->{_inputs}->[0]->{weight});
my $b2 = intr($self->{mesh}->[$_]->{_inputs}->[1]->{weight});
$f=1 if( $b1 && $b2);
$f=2 if(!$b1 && !$b2);
my $lo = $self->{_last_output};
if($lo!=$target) {
# Adjust right lead if $lo, else adjust left lead
($target && $lo)?$self->{_inputs}->[0]->{weight}++:$self->{_inputs}->[0]->{weight}--;
($target && !$lo)?$self->{_inputs}->[1]->{weight}++:$self->{_inputs}->[1]->{weight}--;
}
# Thanks to Rolf Mandersheidd for this set of nested conditions on one line
# This determines heuristic error responsibilty on the children
# and recurses the error up the tree.
if($lo!=$target || $f!=($lo?1:2)) {
$self->{_inputs}->[1]->{node}->adjust_weight($inc,$target) if($self->{_inputs}->[1]->{node});
} else {
$self->{_inputs}->[0]->{node}->adjust_weight($inc,$target) if($self->{_inputs}->[1]->{node});
}
};
# Set our custom node connector
$AI::NeuralNet::Mesh::Connector = 'main::_c_tree';
# Create a new network from our specs
my $net = AI::NeuralNet::Mesh->new($specs);
$net->{_original_specs} = $specs;
# Return our new network
return $net;
}
# Our custom node connector for the tree function, above.
# This connects every two nodes from the first range
# to one node of the second range. This is only meant
# to be used in a factored layer mesh, such as one with a
# [8,4,2,1] node specification array. You should never
# worry about what the node spec array is, as that is
# built by tree().
sub _c_tree {
my ($self,$r1a,$r1b,$r2a,$r2b)=@_;
my $mesh = $self->{mesh};
my $z=$r2a;
for(my $y=0;$y<($r1b-$r1a);$y+=2) {
$mesh->[$y]->add_output_node($mesh->[$z]);
$mesh->[$y+1]->add_output_node($mesh->[$z]);
$z++;
}
}
examples/ex_alpha.pl view on Meta::CPAN
=begin
File: examples/ex_alpha.pl
Author: Josiah Bryan, <jdb@wcoil.com>
Desc:
This demonstrates the ability of a neural net to
generalize and predict what the correct result is
for inputs that it has never seen before.
This teaches the network to classify some twenty-
nine seperate 35-byte bitmaps, and then it inputs
an never-before-seen bitmap and displays the
classification the network gives for the unknown bitmap.
=cut
use AI::NeuralNet::Mesh;
# Create a new network with 35 neurons in input layer and 1 output neuron
my $net = new AI::NeuralNet::Mesh([
{
nodes => 35,
activation => linear
},
{
nodes => 1,
activation => linear,
}
]);
# Debug level of 4 gives JUST learn loop iteteration benchmark and comparrison data
# as learning progresses.
$net->debug(4);
my $letters = [ # All prototype inputs
[
0,1,1,1,0, # Inputs are
1,0,0,0,1, # 5*7 digitalized caracters
1,0,0,0,1,
1,1,1,1,1,
1,0,0,0,1, # This is the alphabet of the
1,0,0,0,1, # HP 28S
1,0,0,0,1,
],[0],[
1,1,1,1,0,
1,0,0,0,1,
1,0,0,0,1,
1,1,1,1,0,
1,0,0,0,1,
1,0,0,0,1,
1,1,1,1,0,
],[1],[
0,1,1,1,0,
1,0,0,0,1,
1,0,0,0,0,
1,0,0,0,0,
1,0,0,0,0,
1,0,0,0,1,
0,1,1,1,0,
],[2],[
1,1,1,0,0,
1,0,0,1,0,
1,0,0,0,1,
1,0,0,0,1,
1,0,0,0,1,
1,0,0,1,0,
1,1,1,0,0,
],[4],[
1,1,1,1,1,
1,0,0,0,0,
1,0,0,0,0,
1,1,1,1,0,
1,0,0,0,0,
1,0,0,0,0,
1,1,1,1,1,
],[5],[
1,1,1,1,1,
1,0,0,0,0,
1,0,0,0,0,
1,1,1,1,0,
1,0,0,0,0,
1,0,0,0,0,
1,0,0,0,0,
],[6],[
0,1,1,1,0,
1,0,0,0,1,
1,0,0,0,0,
1,0,0,0,0,
1,0,0,1,1,
1,0,0,0,1,
0,1,1,1,0,
],[7],[
1,0,0,0,1,
1,0,0,0,1,
1,0,0,0,1,
1,1,1,1,1,
1,0,0,0,1,
1,0,0,0,1,
1,0,0,0,1,
],[8],[
1,1,1,1,1,
0,1,1,1,0,
0,1,1,1,0,
0,1,1,1,0,
0,1,1,1,0,
0,1,1,1,0,
1,1,1,1,1,
],[9],[
0,0,0,0,1,
0,0,0,0,1,
0,0,0,0,1,
0,0,0,0,1,
0,0,0,0,1,
1,0,0,0,1,
0,1,1,1,0,
],[10],[
1,0,0,0,1,
1,0,0,0,1,
1,0,0,1,0,
1,1,1,0,0,
1,0,0,1,0,
1,0,0,0,1,
1,0,0,0,1,
],[11],[
1,0,0,0,0,
1,0,0,0,0,
1,0,0,0,0,
1,0,0,0,0,
1,0,0,0,0,
1,0,0,0,0,
1,1,1,1,1,
],[12],[
1,0,0,0,1,
1,1,0,1,1,
1,0,1,0,1,
1,0,0,0,1,
1,0,0,0,1,
1,0,0,0,1,
1,0,0,0,1,
],[13],[
1,0,0,0,1,
1,0,0,0,1,
1,1,0,0,1,
1,0,1,0,1,
1,0,0,1,1,
1,0,0,0,1,
1,0,0,0,1,
],[14],[
0,1,1,1,0,
1,0,0,0,1,
1,0,0,0,1,
1,0,0,0,1,
1,0,0,0,1,
1,0,0,0,1,
0,1,1,1,0,
],[15],[
1,1,1,1,0,
1,0,0,0,1,
1,0,0,0,1,
1,1,1,1,0,
1,0,0,0,0,
1,0,0,0,0,
1,0,0,0,0,
],[16],[
0,1,1,1,0,
1,0,0,0,1,
1,0,0,0,1,
1,0,0,0,1,
1,0,1,0,1,
1,0,0,1,0,
0,1,1,0,1,
],[17],[
1,1,1,1,0,
1,0,0,0,1,
1,0,0,0,1,
1,1,1,1,0,
1,0,1,0,0,
1,0,0,1,0,
1,0,0,0,1,
],[18],[
0,1,1,1,0,
1,0,0,0,1,
1,0,0,0,0,
0,1,1,1,0,
0,0,0,0,1,
1,0,0,0,1,
0,1,1,1,0,
],[19],[
1,1,1,1,1,
0,0,1,0,0,
0,0,1,0,0,
0,0,1,0,0,
0,0,1,0,0,
0,0,1,0,0,
0,0,1,0,0,
],[20],[
1,0,0,0,1,
1,0,0,0,1,
1,0,0,0,1,
1,0,0,0,1,
1,0,0,0,1,
1,0,0,0,1,
0,1,1,1,0,
],[21],[
1,0,0,0,1,
1,0,0,0,1,
1,0,0,0,1,
1,0,0,0,1,
1,0,0,0,1,
0,1,0,1,0,
0,0,1,0,0,
],[22],[
1,0,0,0,1,
1,0,0,0,1,
1,0,0,0,1,
1,0,1,0,1,
1,0,1,0,1,
1,1,0,1,1,
1,0,0,0,1,
],[23],[
1,0,0,0,1,
1,0,0,0,1,
0,1,0,1,0,
0,0,1,0,0,
0,1,0,1,0,
1,0,0,0,1,
1,0,0,0,1,
],[24],[
1,0,0,0,1,
1,0,0,0,1,
0,1,0,1,0,
0,0,1,0,0,
0,0,1,0,0,
0,0,1,0,0,
0,0,1,0,0,
],[25],[
1,1,1,1,1,
0,0,0,0,1,
0,0,0,1,0,
0,0,1,0,0,
0,1,0,0,0,
1,0,0,0,0,
1,1,1,1,1,
],[26],[
0,0,1,0,0,
0,1,1,1,0,
0,1,0,1,0,
1,1,0,1,1,
1,1,1,1,1,
1,1,0,1,1,
1,0,0,0,1,
],[27],[
1,0,0,0,1,
0,1,0,0,1,
0,0,1,1,0,
0,0,1,1,0,
0,0,1,0,0,
0,1,0,0,0,
1,0,0,0,0,
],[28],[
1,0,0,0,1,
1,0,0,0,1,
1,0,1,0,1,
1,1,1,1,1,
1,1,1,1,1,
0,1,0,1,0,
0,1,0,1,0,
],[29],[
1,0,0,0,1,
1,0,0,0,1,
1,0,0,0,1,
1,1,0,1,1,
0,1,0,1,0,
0,1,1,1,0,
0,0,1,0,2
]
];
if(!$net->load("alpha.mesh")) {
#$net->range(0..29);
$net->learn_set($letters);
$net->save("alpha.mesh");
}
# Build a test map
my $tmp = [0,1,1,1,0,
1,0,0,0,1,
1,0,0,0,1,
1,1,1,1,1,
1,0,0,0,1,
1,0,0,0,1,
1,0,0,0,1];
# Display test map
print "\nTest map:\n";
$net->join_cols($tmp,5);
# Display network results
print "Letter index matched: ",$net->run($tmp)->[0],"\n";
examples/ex_and.pl view on Meta::CPAN
=begin
File: examples/ex_and.pl
Author: Josiah Bryan, <jdb@wcoil.com>
Desc:
This demonstrates a simple AND gate.
Included is example of the hash construction form of the new() method.
=cut
use AI::neuralNet::Mesh;
# Uses 1 layer and 2 nodes per layer, with one output node
my $net = new AI::NeuralNet::Mesh([
{
nodes => 2, # input layer, 2 nodes
activation => linear # linear transfer function
},
{
nodes => 1, # output layer, 1 node
activation => sigmoid, # sigmoid transfer function, (0/1)
threshold => 0.75 # set threshold for sigmoid fn to 0.75
}
]);
if(!$net->load('and.mesh')) {
$net->learn_set([
[1,1], [1],
[1,0], [0],
[0,1], [0],
[0,0], [0],
]);
$net->save('and.mesh');
}
print "Learning complete.\n";
print "Testing with a gate value of (0,0):",$net->run([0,0])->[0],"\n";
print "Testing with a gate value of (0,1):",$net->run([0,1])->[0],"\n";
print "Testing with a gate value of (1,0):",$net->run([1,0])->[0],"\n";
print "Testing with a gate value of (1,1):",$net->run([1,1])->[0],"\n";
examples/ex_bmp.pl view on Meta::CPAN
=begin
File: examples/ex_bmp.pl
Author: Josiah Bryan, <jdb@wcoil.com>
Desc:
This demonstrates simple classification of 6x6 bitmaps.
=cut
use AI::NeuralNet::Mesh;
use Benchmark;
# Set resolution
my $xres=5;
my $yres=5;
# Create a new net with 3 layes, $xres*$yres inputs, and 1 output
my $net = AI::NeuralNet::Mesh->new(1,$xres*$yres,1);
# Enable debugging
$net->debug(4);
# Create datasets.
my @data = (
[ 0,1,1,0,0,
0,0,1,0,0,
0,0,1,0,0,
0,0,1,0,0,
0,1,1,1,2 ], [ 1 ],
[ 1,1,1,0,0,
0,0,0,1,0,
0,1,1,1,0,
1,0,0,0,0,
1,1,1,1,2 ], [ 2 ],
[ 0,1,1,1,0,
1,0,0,0,0,
1,1,1,0,0,
1,0,0,0,0,
0,1,1,1,2 ], [ 3 ],
[ 1,0,0,1,0,
1,0,0,1,0,
1,1,1,1,0,
0,0,0,1,0,
0,0,0,1,2 ], [ 4 ],
[ 1,1,1,1,0,
1,0,0,0,0,
1,1,1,1,0,
0,0,0,1,0,
1,1,1,1,2 ], [ 5 ],
);
# If we havnt saved the net already, do the learning
if(!$net->load('images.mesh')) {
print "\nLearning started...\n";
# Make it learn the whole dataset $top times
my @list;
my $top=3;
for my $a (0..$top) {
my $t1=new Benchmark;
print "\n\nOuter Loop: $a\n";
# Test fogetfullness
my $f = $net->learn_set(\@data, inc => 0.1);
# Print it
print "\n\nForgetfullness: $f%\n";
# Save net to disk
$net->save('images.mesh');
my $t2=new Benchmark;
my $td=timediff($t0,$t1);
print "\nLoop $a took ",timestr($td),"\n";
}
}
my @set=( 0,1,1,1,0,
1,0,0,0,0,
1,1,1,0,0,
1,0,0,0,0,
0,1,1,1,2 );
# Image number
my $fb=$net->run(\@set)->[0];
# Print output
print "\nTest Map: \n";
$net->join_cols(\@set,5);
print "Image number matched: $fb\n";
examples/ex_bmp2.pl view on Meta::CPAN
=begin
File: examples/ex_bmp2.pl
Author: Josiah Bryan, <jdb@wcoil.com>
Desc:
This demonstrates the ability of a neural net
to generalize and predict what the correct
result is for inputs that it has never seen before.
This teaches a network to recognize a 5x7 bitmap of
the letter "J" then it presents the network with a
corrupted "J" and displays the results of the networks
output.
=cut
use AI::NeuralNet::Mesh;
# Create a new network with 2 layers and 35 neurons in each layer.
my $net = new AI::NeuralNet::Mesh(1,35,1);
# Debug level of 4 gives JUST learn loop iteteration benchmark and comparrison data
# as learning progresses.
$net->debug(4);
# Create our model input
my @map = (1,1,1,1,1,
0,0,1,0,0,
0,0,1,0,0,
0,0,1,0,0,
1,0,1,0,0,
1,0,1,0,0,
1,1,1,0,0);
print "\nLearning started...\n";
print $net->learn(\@map,'J');
print "Learning done.\n";
# Build a test map
my @tmp = (0,0,1,1,1,
1,1,1,0,0,
0,0,0,1,0,
0,0,0,1,0,
0,0,0,1,0,
0,0,0,0,0,
0,1,1,0,0);
# Display test map
print "\nTest map:\n";
$net->join_cols(\@tmp,5,'');
print "Running test...\n";
# Run the actual test and get network output
print "Result: ",$net->run_uc(\@tmp),"\n";
print "Test run complete.\n";
examples/ex_crunch.pl view on Meta::CPAN
=begin
File: examples/ex_crunch.pl
Author: Josiah Bryan, jdb@wcoil.com
Desc:
This demonstrates the crunch() and uncrunch() methods.
=cut
use AI::NeuralNet::Mesh;
my $net = AI::NeuralNet::Mesh->new(2,3);
# Here crunch is good for storing sentance crunches
my $bad = $net->crunch("That's Junk Food!");
my $good = $net->crunch("Good, Healthy Food.");
my $set = [
"I love chips.", $bad,
"I love apples.", $good,
"I love pop.", $bad,
"I love oranges.", $good
];
#$net->debug(4);
for (0..2) {
my $f = $net->learn_set($set);
print "Forgotten: $f%\n";
}
# run() automatically crunches the string (run_uc() uses run() internally) and
# run_uc() automatically uncrunches the results.
print $net->run_uc("I love pop-tarts.");
examples/ex_dow.pl view on Meta::CPAN
=begin
File: examples/ex_dow.pl
Author: Josiah Bryan, <jdb@wcoil.com>
Desc:
This demonstrates DOW Avg. predicting using the
AI::NeuralNet::Mesh module.
=cut
use AI::NeuralNet::Mesh;
use Benchmark;
# Create a new net with 5 layes, 9 inputs, and 1 output
my $net = AI::NeuralNet::Mesh->new(2,9,1);
# Disable debugging
$net->debug(2);
# Create datasets.
# Note that these are ficticious values shown for illustration purposes
# only. In the example, CPI is a certain month's consumer price
# index, CPI-1 is the index one month before, CPI-3 is the the index 3
# months before, etc.
my @data = (
# Mo CPI CPI-1 CPI-3 Oil Oil-1 Oil-3 Dow Dow-1 Dow-3 Dow Ave (output)
[ 1, 229, 220, 146, 20.0, 21.9, 19.5, 2645, 2652, 2597], [ 2647 ],
[ 2, 235, 226, 155, 19.8, 20.0, 18.3, 2633, 2645, 2585], [ 2637 ],
[ 3, 244, 235, 164, 19.6, 19.8, 18.1, 2627, 2633, 2579], [ 2630 ],
[ 4, 261, 244, 181, 19.6, 19.6, 18.1, 2611, 2627, 2563], [ 2620 ],
[ 5, 276, 261, 196, 19.5, 19.6, 18.0, 2630, 2611, 2582], [ 2638 ],
[ 6, 287, 276, 207, 19.5, 19.5, 18.0, 2637, 2630, 2589], [ 2635 ],
[ 7, 296, 287, 212, 19.3, 19.5, 17.8, 2640, 2637, 2592], [ 2641 ]
);
# If we havnt saved the net already, do the learning
if(!$net->load('DOW.mesh')) {
print "\nLearning started...\n";
# Make it learn the whole dataset $top times
my @list;
my $top=1;
for my $a (0..$top) {
my $t1=new Benchmark;
print "\n\nOuter Loop: $a\n";
# Test fogetfullness
my $f = $net->learn_set(\@data, inc => 0.2,
max => 2000,
error => -1);
# Print it
print "\n\nForgetfullness: $f%\n";
# Save net to disk
$net->save('DOW.mesh');
my $t2=new Benchmark;
my $td=timediff($t2,$t1);
print "\nLoop $a took ",timestr($td),"\n";
}
}
# Run a prediction using fake data
# Month CPI CPI-1 CPI-3 Oil Oil-1 Oil-3 Dow Dow-1 Dow-3
my @set=( 10, 352, 309, 203, 18.3, 18.7, 16.1, 2592, 2641, 2651 );
# Dow Ave (output)
my $fb=$net->run(\@set)->[0];
# Print output
print "\nTest Factors: (",join(',',@set),")\n";
print "DOW Prediction for Month #11: $fb\n";
examples/ex_mult.pl view on Meta::CPAN
=begin
File: examples/ex_mult.pl
Author: Josiah Bryan, <jdb@wcoil.com>
Desc:
This demonstrates the ability of a neural net to generalize and predict what the correct
result is for inputs that it has never seen before.
This teaches a network to multiply 6 sets of numbers, then it asks the user for
two numbers to multiply and then it displays the results of the user's input.
=cut
use AI::NeuralNet::Mesh;
my $multiply = new AI::NeuralNet::Mesh(2,2,1);
if(!$multiply->load('mult.mesh')) {
$multiply->learn_set([
[ 1, 1 ], [ 1 ] ,
[ 2, 1 ], [ 2 ],
[ 2, 2 ], [ 4 ],
[ 2, 4 ], [ 8 ],
[ 2, 8 ], [ 16 ],
[ 9, 9 ], [ 81 ],
[ 10, 5 ], [ 50 ],
[ 20, 10 ], [ 200 ],
[ 100, 50 ], [ 5000 ],
]);
$multiply->save('mult.mesh');
}
print "Enter first number to multiply : "; chomp(my $a = <>);
print "Enter second number to multiply : "; chomp(my $b = <>);
print "Result: ",$multiply->run([$a,$b])->[0],"\n";
examples/ex_or.pl view on Meta::CPAN
=begin
File: examples/ex_and.pl
Author: Josiah Bryan, <jdb@wcoil.com>
Desc:
This demonstrates a simple OR gate.
This is an intersting function of the network, as it functions
as an OR gate with no learning and only a sigmoid transfer function
on the output node.
=cut
use AI::neuralNet::Mesh;
# Uses 1 layer and 2 nodes per layer, with one output node
my $net = new AI::NeuralNet::Mesh(1,2,1);
# Example of alternate ways to set activation and thresholds
$net->activation(1,sigmoid);
$net->threshold( 1,0.5);
if(!$net->load('or.mesh')) {
$net->learn_set([
[1,1], [1],
[1,0], [1],
[0,1], [1],
[0,0], [0],
]);
$net->save('or.mesh');
}
print "Learning complete.\n";
print "Testing with a gate value of (0,0):",$net->run([0,0])->[0],"\n";
print "Testing with a gate value of (0,1):",$net->run([0,1])->[0],"\n";
print "Testing with a gate value of (1,0):",$net->run([1,0])->[0],"\n";
print "Testing with a gate value of (1,1):",$net->run([1,1])->[0],"\n";
examples/ex_pat.pl view on Meta::CPAN
=begin
File: examples/ex_pat.pl
Author: Tobias Bronx, <tobiasb@odin.funcom.com>
Desc:
This demonstrates simply pattern learning.
=cut
use AI::NeuralNet::Mesh;
$net=AI::NeuralNet::Mesh->new(2,2,2);
print $net->learn([2,2],[2,2],max=>3),"\n";
for (0..1) {
for my $a (1..2) {
for my $b (1..2) {
@a=($a,$b);
print join(",",@a),":",join(",",@{$net->run(\@a)}), "\n";
$net->learn(\@a,\@a, max=>100,inc=>0.17);
print join(",",@{$net->run(@a)}),"\n";
}
}
}
print "1,2:",join(",",@{$net->run([1,2])}),"\n";
examples/ex_pcx.pl view on Meta::CPAN
=begin
File: examplex/ex_pcx.pl
Author: Josiah Bryan, <jdb@wcoil.com>
Desc:
This teaches the network to classify
10x10 bitmaps from a PCX file based on their
whiteness. (This was taught on a b&w 320x200
PCX of the author at an early age :-)
=cut
use AI::NeuralNet::Mesh;
# Set block sizes
my ($bx,$by)=(10,10);
print "Creating Neural Net...";
my $net=AI::NeuralNet::Mesh->new(1,$bx*$by,1);
$net->{col_width} = $bx;
print "Done!\n";
print "Loading bitmap...";
my $img = $net->load_pcx("josiah.pcx");
print "Done!\n";
print "Comparing blocks...\n";
my $white = $img->get_block([0,0,$bx,$by]);
my ($x,$y,$tmp,@scores,$s,@blocks,$b);
for ($x=0;$x<320;$x+=$bx) {
for ($y=0;$y<200;$y+=$by) {
$blocks[$b++]=$img->get_block([$x,$y,$x+$bx,$y+$by]);
$score[$s++]=$net->pdiff($white,$blocks[$b-1]);
print "Block at [$x,$y], index [$s] scored ".$score[$s-1]."%\n";
}
}
print "Done!";
print "High score:\n";
print_ref($blocks[$net->high(\@score)],$bx);
print "Low score:\n";
print_ref($blocks[$net->low(\@score)],$bx);
$net->debug(4);
if(!$net->load("pcx.mesh")) {
print "Learning high block...\n";
print $net->learn($blocks[$net->high(\@score)],"highest");
$net->save("pcx.mesh");
print "Learning low block...\n";
$net->learn($blocks[$net->low(\@score)],"lowest");
}
print "Testing random block...\n";
print "Result: ",$net->run($blocks[rand()*$b])->[0],"\n";
print "Bencmark for run: ", $net->benchmarked(), "\n";
$net->save("pcx2.net");
sub print_ref {
no strict 'refs';
shift if(substr($_[0],0,4) eq 'AI::');
my $map = shift;
my $break = shift;
my $x;
my @els = (' ','.',',',':',';','%','#');
foreach my $el (@{$map}) {
$str=$el/255*6;
print $els[$str];
$x++;
if($x>$break-1) {
print "\n";
$x=0;
}
}
print "\n";
}
examples/ex_pcxl.pl view on Meta::CPAN
=begin
File: examples/ex_pcxl.pl
Author: Josiah Bryan, jdb@wcoil.com
Desc:
This just demonstrates simple usage of the pcx loader.
=cut
use AI::NeuralNet::Mesh;
my $net=AI::NeuralNet::Mesh->new(2,2);
my $img = $net->load_pcx("josiah.pcx");
print "ERROR: ",$net->error(),"\n" if($net->error());
$net->join_cols($img->get_block([0,0,50,50]),50,0);
examples/ex_sub.pl view on Meta::CPAN
=begin
File: examples/ex_sub.pl
Author: Josiah Bryan, <jdb@wcoil.com>
Desc:
This demonstrates the ability of a neural net to generalize and predict what the correct
result is for inputs that it has never seen before.
This teaches a network to subtract 6 sets of numbers, then it asks the user for
two numbers to subtract and then it displays the results of the user's input.
=cut
use AI::NeuralNet::Mesh;
my $subtract = new AI::NeuralNet::Mesh(2,2,1);
if(!$subtract->load('sub.mesh')) {
$subtract->learn_set([
[ 1, 1 ], [ 0 ] ,
[ 2, 1 ], [ 1 ],
[ 10, 5 ], [ 5 ],
[ 20, 10 ], [ 10 ],
[ 100, 50 ], [ 50 ],
[ 500, 200 ], [ 300 ],
]);
$subtract->save('sub.mesh');
}
print "Enter first number to subtract : "; chomp(my $a = <>);
print "Enter second number to subtract : "; chomp(my $b = <>);
print "Result: ",$subtract->run([$a,$b])->[0],"\n";
examples/ex_synop.pl view on Meta::CPAN
=begin
File: examples/ex_synop.pl
Author: Josiah Bryan, <jdb@wcoil.com>
Desc:
This is the synopsis from the POD for AI::NeuralNet::BackProp.
=cut
use AI::NeuralNet::Mesh;
# Create a new network with 1 layer, 5 inputs, and 5 outputs.
my $net = new AI::NeuralNet::Mesh(1,5,5);
# Add a small amount of randomness to the network
$net->random(0.001);
# Demonstrate a simple learn() call
my @inputs = ( 0,0,1,1,1 );
my @ouputs = ( 1,0,1,0,1 );
print $net->learn(\@inputs, \@outputs),"\n";
# Create a data set to learn
my @set = (
[ 2,2,3,4,1 ], [ 1,1,1,1,1 ],
[ 1,1,1,1,1 ], [ 0,0,0,0,0 ],
[ 1,1,1,0,0 ], [ 0,0,0,1,1 ]
);
# Demo learn_set()
my $f = $net->learn_set(\@set);
print "Forgetfulness: $f unit\n";
# Crunch a bunch of strings and return array refs
my $phrase1 = $net->crunch("I love neural networks!");
my $phrase2 = $net->crunch("Jay Lenno is wierd.");
my $phrase3 = $net->crunch("The rain in spain...");
my $phrase4 = $net->crunch("Tired of word crunching yet?");
# Make a data set from the array refs
my @phrases = (
$phrase1, $phrase2,
$phrase3, $phrase4
);
# Learn the data set
$net->learn_set(\@phrases);
# Run a test phrase through the network
my $test_phrase = $net->crunch("I love neural networking!");
my $result = $net->run($test_phrase);
# Get this, it prints "Jay Leno is networking!" ... LOL!
print $net->uncrunch($result),"\n";
examples/ex_wine.pl view on Meta::CPAN
=begin
File: examples/ex_wine.pl
Author: Josiah Bryan, <jdb@wcoil.com>
Desc:
This demonstrates wine cultivar prediction using the
AI::NeuralNet::Mesh module.
This script uses the data that is the results of a chemical analysis
of wines grown in the same region in Italy but derived from three
different cultivars. The analysis determined the quantities
of 13 constituents found in each of the three types of wines.
The inputs of the net represent 13 seperate attributes
of the wine's chemical analysis, as follows:
1) Alcohol
2) Malic acid
3) Ash
4) Alcalinity of ash
5) Magnesium
6) Total phenols
7) Flavanoids
8) Nonflavanoid phenols
9) Proanthocyanins
10) Color intensity
11) Hue
12) OD280/OD315 of diluted wines
13) Proline
There are 168 total examples, with the class distrubution
as follows:
class 1: 59 instances
class 2: 71 instances
class 3: 48 instances
The datasets are stored in wine.dat, and the first
column on every row is the class attribute for that
row.
=cut
use AI::NeuralNet::Mesh;
use Benchmark;
# Create a new net
my $net = AI::NeuralNet::Mesh->new([13,45,1]);
# Set activation on output node to contstrain values
# to a specific range of values.
$net->activation(2,range(1..3));
# Enable debugging
$net->verbose(4);
# Load the data set
my $data = $net->load_set('wine.dat',0);
# Seperate data based on class
my $sets=[];
for my $i (0..$#{$data}/2) {
my $c = $data->[$i*2+1]->[0];
print "Class of set $i: $c \r";
# inputs
$sets->[$c]->[++$#{$sets->[$c]}] = $data->[$i*2];
# class
$sets->[$c]->[++$#{$sets->[$c]}] = $data->[$i*2+1];
}
for(0..$#{$sets}) {
next if(!defined $sets->[$_]->[0]);
print "Size of set $_: ",$#{$sets->[$_]}/2,"\n";
}
# If we havnt saved the net already, do the learning
if(!$net->load('wine.mesh')) {
print "\nLearning started...\n";
# Make it learn the whole dataset $top times
my @list;
my $top=5;
for my $a (0..$top) {
print "\n\nOuter Loop: $a\n";
for(0..$#{$sets}) {
next if(!defined $sets->[$_]->[0]);
my $t1=new Benchmark;
# Test fogetfullness
my $f = $net->learn_set($sets->[$_], inc => 0.2,
max => 2000,
error => 0.01,
leave => 2);
# Print it
print "\n\nForgetfullness: $f%\n";
my $t2=new Benchmark;
my $td=timediff($t2,$t1);
print "\nLoop [$a,$_] took ",timestr($td),"\n";
}
# Save net to disk
$net->save('wine.mesh');
}
}
# Set activation on output node to contstrain values
# to a specific range of values.
$net->activation(2,range(1..3));
my @cnts;
for(0..$#{$sets}) {
next if(!defined $sets->[$_]->[0]);
my $s=$#{$sets->[$_]}/2;
my $cnt=0;
print "Set: $_\n";
my $results=$net->run_set($sets->[$_]);
for my $x (0..$s-1) {
$cnt++ if($results->[$x]->[0]==$_);
}
$cnts[$_]=$cnt;
}
for(0..$#{$sets}) {
next if(!defined $sets->[$_]->[0]);
my $s=$#{$sets->[$_]}/2;
print "Class $_: $cnts[$_] correct out of $s (",$net->p($cnts[$_],$s),"%).\n";
}
examples/wine.dat view on Meta::CPAN
3,13.58,2.58,2.69,24.5,105,1.55,.84,.39,1.54,8.66,.74,1.8,750
3,13.4,4.6,2.86,25,112,1.98,.96,.27,1.11,8.5,.67,1.92,630
3,12.2,3.03,2.32,19,96,1.25,.49,.4,.73,5.5,.66,1.83,510
3,12.77,2.39,2.28,19.5,86,1.39,.51,.48,.64,9.899999,.57,1.63,470
3,14.16,2.51,2.48,20,91,1.68,.7,.44,1.24,9.7,.62,1.71,660
3,13.71,5.65,2.45,20.5,95,1.68,.61,.52,1.06,7.7,.64,1.74,740
3,13.4,3.91,2.48,23,102,1.8,.75,.43,1.41,7.3,.7,1.56,750
3,13.27,4.28,2.26,20,120,1.59,.69,.43,1.35,10.2,.59,1.56,835
3,13.17,2.59,2.37,20,120,1.65,.68,.53,1.46,9.3,.6,1.62,840
3,14.13,4.1,2.74,24.5,96,2.05,.76,.56,1.35,9.2,.61,1.6,560
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<B>AI::NeuralNet::Mesh</B> - An optimized, accurate neural network Mesh.
</PRE>
<A NAME="__index__"></A>
<!-- INDEX BEGIN -->
<UL>
<LI><A HREF="#name">NAME</A></LI>
<LI><A HREF="#synopsis">SYNOPSIS</A></LI>
<LI><A HREF="#version & updates">VERSION & UPDATES</A></LI>
<LI><A HREF="#description">DESCRIPTION</A></LI>
<LI><A HREF="#exports">EXPORTS</A></LI>
<LI><A HREF="#methods">METHODS</A></LI>
<LI><A HREF="#custom activation functions">CUSTOM ACTIVATION FUNCTIONS</A></LI>
<LI><A HREF="#variables">VARIABLES</A></LI>
<LI><A HREF="#custom network connectors">CUSTOM NETWORK CONNECTORS</A></LI>
<LI><A HREF="#what can it do">WHAT CAN IT DO?</A></LI>
<LI><A HREF="#examples">EXAMPLES</A></LI>
<LI><A HREF="#other included packages">OTHER INCLUDED PACKAGES</A></LI>
<LI><A HREF="#bugs">BUGS</A></LI>
<LI><A HREF="#author">AUTHOR</A></LI>
<LI><A HREF="#thanks">THANKS</A></LI>
<LI><A HREF="#download">DOWNLOAD</A></LI>
<LI><A HREF="#mailing list">MAILING LIST</A></LI>
</UL>
<!-- INDEX END -->
<HR>
<P>
<H1><A NAME="name">NAME</A></H1>
<P>AI::NeuralNet::Mesh - An optimized, accurate neural network Mesh.</P>
<P>
<HR>
<H1><A NAME="synopsis">SYNOPSIS</A></H1>
<PRE>
use AI::NeuralNet::Mesh;
# Create a mesh with 2 layers, 2 nodes/layer, and one output node.
my $net = new AI::NeuralNet::Mesh(2,2,1);
# Teach the network the AND function
$net->learn([0,0],[0]);
$net->learn([0,1],[0]);
$net->learn([1,0],[0]);
$net->learn([1,1],[1]);
# Present it with two test cases
my $result_bit_1 = $net->run([0,1])->[0];
my $result_bit_2 = $net->run([1,1])->[0];
# Display the results
print "AND test with inputs (0,1): $result_bit_1\n";
print "AND test with inputs (1,1): $result_bit_2\n";
</PRE>
<P>
<HR>
<H1><A NAME="version & updates">VERSION & UPDATES</A></H1>
<P>This is version <STRONG>0.43</STRONG>, the second release of this module.</P>
<P>With this version I have gone through and tuned up many area
of this module, including the descent algorithim in learn(),
as well as four custom activation functions, and several export
tag sets. With this release, I have also included a few
new and more practical example scripts. (See ex_wine.pl) This release
mesh. This form preforms descent toward a local error minimum (0) on a
directional delta, rather than the desired value for that node. This allows
for better, and more accurate results with larger datasets. This module also
uses a simpler recursion technique which, suprisingly, is more accurate than
the original technique that I've used in other ANNs.</P>
<P>
<HR>
<H1><A NAME="exports">EXPORTS</A></H1>
<P>This module exports three functions by default:</P>
<PRE>
range
intr
pdiff
</PRE>
<P>See range() intr() and pdiff() for description of their respective functions.</P>
<P>Also provided are several export tag sets for usage in the form of:</P>
<PRE>
use AI::NeuralNet::Mesh ':tag';
</PRE>
<P>Tag sets are:</P>
<PRE>
:default
- These functions are always exported.
- Exports:
range()
intr()
pdiff()
:all
- Exports:
p()
high()
low()
range()
ramp()
and_gate()
or_gate()
:p
- Exports:
p()
high()
low()
:acts
- Exports:
ramp()
and_gate()
or_gate()
</PRE>
<P>See the respective methods/functions for information about
each method/functions usage.</P>
<P>
<HR>
<H1><A NAME="methods">METHODS</A></H1>
<DL>
<DT><STRONG><A NAME="item_new">AI::NeuralNet::Mesh->new();</A></STRONG><BR>
<DD>
There are four ways to construct a new network with new(). Each is detailed below.
<P></P>
<DT><STRONG>AI::NeuralNet::Mesh->new(\@layer_sizes);</STRONG><BR>
<DD>
This constructor will make a network with the number of layers corresponding to the length
in elements of the array ref passed. Each element in the array ref passed is expected
to contain an integer specifying the number of nodes (neurons) in that layer. The first
layer ($layer_sizes[0]) is to be the input layer, and the last layer in @layer_sizes is to be
the output layer.
<P>Example:</P>
<PRE>
my $net = AI::NeuralNet::Mesh->new([2,3,1]);</PRE>
<P>Creates a network with 2 input nodes, 3 hidden nodes, and 1 output node.</P>
<P></P>
<DT><STRONG>AI::NeuralNet::Mesh->new(\@array_of_hashes);</STRONG><BR>
<DD>
Another dandy constructor...this is my favorite. It allows you to tailor the number of layers,
the size of the layers, the activation type (you can even add anonymous inline subs with this one),
and even the threshold, all with one array ref-ed constructor.
<P>Example:</P>
<PRE>
my $net = AI::NeuralNet::Mesh->new([
{
nodes => 2,
activation => linear
},
{
nodes => 3,
activation => sub {
my $sum = shift;
return $sum + rand()*1;
}
},
{
nodes => 1,
activation => sigmoid,
threshold => 0.75
}
]);
</PRE>
<P>Interesting, eh? What you are basically passing is this:</P>
<PRE>
my @info = (
{ },
{ },
{ },
...
);</PRE>
<P>You are passing an array ref who's each element is a hash refrence. Each
hash refrence, or more precisely, each element in the array refrence you are passing
to the constructor, represents a layer in the network. Like the constructor above,
the first element is the input layer, and the last is the output layer. The rest are
hidden layers.</P>
<P>Each hash refrence is expected to have AT LEAST the ``nodes'' key set to the number
of nodes (neurons) in that layer. The other two keys are optional. If ``activation'' is left
out, it defaults to ``linear''. If ``threshold'' is left out, it defaults to 0.50.</P>
<P>The ``activation'' key can be one of four values:</P>
<PRE>
linear ( simply use sum of inputs as output )
sigmoid [ sigmoid_1 ] ( only positive sigmoid )
sigmoid_2 ( positive / 0 /negative sigmoid )
\&code_ref;</PRE>
<P>``sigmoid_1'' is an alias for ``sigmoid''.</P>
<P>The code ref option allows you to have a custom activation function for that layer.
The code ref is called with this syntax:</P>
<PRE>
$output = &$code_ref($sum_of_inputs, $self);
</PRE>
<P>The code ref is expected to return a value to be used as the output of the node.
The code ref also has access to all the data of that node through the second argument,
a blessed hash refrence to that node.</P>
<P>See CUSTOM ACTIVATION FUNCTIONS for information on several included activation functions
other than the ones listed above.</P>
<P>Three of the activation syntaxes are shown in the first constructor above, the ``linear'',
``sigmoid'' and code ref types.</P>
<P>You can also set the activation and threshold values after network creation with the
<A HREF="#item_activation"><CODE>activation()</CODE></A> and <A HREF="#item_threshold"><CODE>threshold()</CODE></A> methods.</P>
<P></P>
<DT><STRONG><A NAME="item_learn">$net->learn($input_map_ref, $desired_result_ref [, options ]);</A></STRONG><BR>
<DD>
NOTE: <A HREF="#item_learn_set"><CODE>learn_set()</CODE></A> now has increment-degrading turned OFF by default. See note
on the degrade flag, below.
<P>This will 'teach' a network to associate an new input map with a desired
result. It will return a string containg benchmarking information.</P>
<P>You can also specify strings as inputs and ouputs to learn, and they will be
crunched automatically. Example:</P>
<PRE>
$net->learn('corn', 'cob');
</PRE>
<P>Note, the old method of calling crunch on the values still works just as well.</P>
<P>The first two arguments may be array refs (or now, strings), and they may be
of different lengths.</P>
<P>Options should be written on hash form. There are three options:
</P>
<PRE>
inc => $learning_gradient
max => $maximum_iterations
error => $maximum_allowable_percentage_of_error
degrade => $degrade_increment_flag</PRE>
<P>$learning_gradient is an optional value used to adjust the weights of the internal
connections. If $learning_gradient is ommitted, it defaults to 0.002.
</P>
<P>$maximum_iterations is the maximum numbers of iteration the loop should do.
It defaults to 1024. Set it to 0 if you never want the loop to quit before
the pattern is perfectly learned.</P>
<P>$maximum_allowable_percentage_of_error is the maximum allowable error to have. If
this is set, then <A HREF="#item_learn"><CODE>learn()</CODE></A> will return when the perecentage difference between the
actual results and desired results falls below $maximum_allowable_percentage_of_error.
If you do not include 'error', or $maximum_allowable_percentage_of_error is set to -1,
the degrade flag wasn't in test.pl, it would take a very long time to learn.</P>
<P></P>
<DT><STRONG><A NAME="item_learn_set">$net->learn_set(\@set, [ options ]);</A></STRONG><BR>
<DD>
This takes the same options as <A HREF="#item_learn"><CODE>learn()</CODE></A> (learn_set() uses <A HREF="#item_learn"><CODE>learn()</CODE></A> internally)
and allows you to specify a set to learn, rather than individual patterns.
A dataset is an array refrence with at least two elements in the array,
each element being another array refrence (or now, a scalar string). For
each pattern to learn, you must specify an input array ref, and an ouput
array ref as the next element. Example:
<PRE>
my @set = (
# inputs outputs
[ 1,2,3,4 ], [ 1,3,5,6 ],
[ 0,2,5,6 ], [ 0,2,1,2 ]
);</PRE>
<P>Inputs and outputs in the dataset can also be strings.</P>
<P>See the paragraph on measuring forgetfulness, below. There are
two learn_set()-specific option tags available:</P>
<PRE>
flag => $flag
pattern => $row</PRE>
<P>If ``flag'' is set to some TRUE value, as in ``flag => 1'' in the hash of options, or if the option ``flag''
is not set, then it will return a percentage represting the amount of forgetfullness. Otherwise,
<A HREF="#item_learn_set"><CODE>learn_set()</CODE></A> will return an integer specifying the amount of forgetfulness when all the patterns
are learned.</P>
<P>If ``pattern'' is set, then <A HREF="#item_learn_set"><CODE>learn_set()</CODE></A> will use that pattern in the data set to measure forgetfulness by.
If ``pattern'' is omitted, it defaults to the first pattern in the set. Example:</P>
<PRE>
my @set = (
[ 0,1,0,1 ], [ 0 ],
[ 0,0,1,0 ], [ 1 ],
[ 1,1,0,1 ], [ 2 ], # <---
[ 0,1,1,0 ], [ 3 ]
);
</PRE>
<P>If you wish to measure forgetfulness as indicated by the line with the arrow, then you would
pass 2 as the "pattern" option, as in "pattern => 2".</P>
<P>Now why the heck would anyone want to measure forgetfulness, you ask? Maybe you wonder how I
even measure that. Well, it is not a vital value that you have to know. I just put in a
``forgetfulness measure'' one day because I thought it would be neat to know.</P>
<P>How the module measures forgetfulness is this: First, it learns all the patterns
in the set provided, then it will run the very first pattern (or whatever pattern
is specified by the ``row'' option) in the set after it has finished learning. It
will compare the <A HREF="#item_run"><CODE>run()</CODE></A> output with the desired output as specified in the dataset.
In a perfect world, the two should match exactly. What we measure is how much that
they don't match, thus the amount of forgetfulness the network has.</P>
<P>Example (from examples/ex_dow.pl):</P>
<PRE>
# Data from 1989 (as far as I know..this is taken from example data on BrainMaker)
my @data = (
# Mo CPI CPI-1 CPI-3 Oil Oil-1 Oil-3 Dow Dow-1 Dow-3 Dow Ave (output)
[ 1, 229, 220, 146, 20.0, 21.9, 19.5, 2645, 2652, 2597], [ 2647 ],
[ 2, 235, 226, 155, 19.8, 20.0, 18.3, 2633, 2645, 2585], [ 2637 ],
[ 3, 244, 235, 164, 19.6, 19.8, 18.1, 2627, 2633, 2579], [ 2630 ],
[ 4, 261, 244, 181, 19.6, 19.6, 18.1, 2611, 2627, 2563], [ 2620 ],
[ 5, 276, 261, 196, 19.5, 19.6, 18.0, 2630, 2611, 2582], [ 2638 ],
[ 6, 287, 276, 207, 19.5, 19.5, 18.0, 2637, 2630, 2589], [ 2635 ],
[ 7, 296, 287, 212, 19.3, 19.5, 17.8, 2640, 2637, 2592], [ 2641 ]
);
# Learn the set
my $f = $net->learn_set(\@data,
inc => 0.1,
max => 500,
);
# Print it
print "Forgetfullness: $f%";</PRE>
<P></P>
<P>This is a snippet from the example script examples/finance.pl, which demonstrates DOW average
prediction for the next month. A more simple set defenition would be as such:</P>
<PRE>
my @data = (
[ 0,1 ], [ 1 ],
[ 1,0 ], [ 0 ]
);
$net->learn_set(\@data);</PRE>
<P>Same effect as above, but not the same data (obviously).</P>
<P></P>
<DT><STRONG><A NAME="item_run">$net->run($input_map_ref);</A></STRONG><BR>
<DD>
This method will apply the given array ref at the input layer of the neural network, and
it will return an array ref to the output of the network. <A HREF="#item_run"><CODE>run()</CODE></A> will now automatically <A HREF="#item_crunch"><CODE>crunch()</CODE></A>
a string given as an input (See the <A HREF="#item_crunch"><CODE>crunch()</CODE></A> method for info on crunching).
<P>Example Usage:
</P>
<PRE>
my $inputs = [ 1,1,0,1 ];
my $outputs = $net->run($inputs);</PRE>
<P>You can also do this with a string:
</P>
<PRE>
my $outputs = $net->run('cloudy - wind is 5 MPH NW');</PRE>
<P>See also <A HREF="#item_run_uc"><CODE>run_uc()</CODE></A> and <A HREF="#item_run_set"><CODE>run_set()</CODE></A> below.</P>
<P></P>
<DT><STRONG><A NAME="item_run_uc">$net->run_uc($input_map_ref);</A></STRONG><BR>
<DD>
This method does the same thing as this code:
<PRE>
$net->uncrunch($net->run($input_map_ref));</PRE>
<P>All that <A HREF="#item_run_uc"><CODE>run_uc()</CODE></A> does is that it automatically calls <A HREF="#item_uncrunch"><CODE>uncrunch()</CODE></A> on the output, regardless
of whether the input was <A HREF="#item_crunch"><CODE>crunch()</CODE></A> -ed or not.</P>
<P></P>
<DT><STRONG><A NAME="item_run_set">$net->run_set($set);</A></STRONG><BR>
<DD>
<P>This takes an array ref of the same structure as the learn_set() method, above. It returns
an array ref. Each element in the returned array ref represents the output for the corresponding
element in the dataset passed. Uses run() internally.</P>
<DT><STRONG><A NAME="item_get_outs">$net->get_outs($set);</A></STRONG><BR>
<DD>
<DD>
See CUSTOM ACTIVATION FUNCTIONS for information on several included activation functions.
<P></P>
<DT><STRONG><A NAME="item_benchmark">$net->benchmark();</A></STRONG><BR>
<DD>
<DT><STRONG><A NAME="item_benchmarked">$net->benchmarked();</A></STRONG><BR>
<DD>
This returns a benchmark info string for the last <A HREF="#item_learn"><CODE>learn()</CODE></A> call.
It is easily printed as a string, as following:
<PRE>
print "Last learn() took ",$net->benchmark(),"\n";</PRE>
<P></P>
<DT><STRONG><A NAME="item_verbose">$net->verbose($level);</A></STRONG><BR>
<DD>
<DT><STRONG><A NAME="item_verbosity">$net->verbosity($level);</A></STRONG><BR>
<DD>
<DT><STRONG><A NAME="item_v">$net->v($level);</A></STRONG><BR>
<DD>
<DT><STRONG><A NAME="item_debug">$net->debug($level)</A></STRONG><BR>
<DD>
Note: verbose(), verbosity(), and <A HREF="#item_v"><CODE>v()</CODE></A> are all functional aliases for debug().
<P>If there were no errors, it will return a refrence to $net.</P>
<P>UPDATE: $filename can now be a newline-seperated set of mesh data. This enables you
to do $net->load(join(``\n'',<DATA>)) and other fun things. I added this mainly
for a demo I'm writing but not qutie done with yet. So, Cheers!</P>
<P></P>
<DT><STRONG><A NAME="item_activation">$net->activation($layer,$type);</A></STRONG><BR>
<DD>
This sets the activation type for layer <CODE>$layer</CODE>.
<P><CODE>$type</CODE> can be one of four values:</P>
<PRE>
linear ( simply use sum of inputs as output )
sigmoid [ sigmoid_1 ] ( only positive sigmoid )
sigmoid_2 ( positive / 0 /negative sigmoid )
\&code_ref;</PRE>
<P>``sigmoid_1'' is an alias for ``sigmoid''.</P>
<P>The code ref option allows you to have a custom activation function for that layer.
The code ref is called with this syntax:</P>
<PRE>
$output = &$code_ref($sum_of_inputs, $self);
</PRE>
<P>The code ref is expected to return a value to be used as the output of the node.
The code ref also has access to all the data of that node through the second argument,
a blessed hash refrence to that node.</P>
<P>See CUSTOM ACTIVATION FUNCTIONS for information on several included activation functions
other than the ones listed above.</P>
<P>The activation type for each layer is preserved across load/save calls.</P>
<P>EXCEPTION: Due to the constraints of Perl, I cannot load/save the actual subs that the code
ref option points to. Therefore, you must re-apply any code ref activation types after a
<A HREF="#item_load"><CODE>load()</CODE></A> call.</P>
undefined string, it <A HREF="#item_join_cols"><CODE>join_cols()</CODE></A> will just print the numerical value of each element seperated
by a null character (\0). <A HREF="#item_join_cols"><CODE>join_cols()</CODE></A> defaults to the latter behaviour.
<P></P>
<DT><STRONG><A NAME="item_extend">$net->extend(\@array_of_hashes);</A></STRONG><BR>
<DD>
This allows you to re-apply any activations and thresholds with the same array ref which
you created a network with. This is useful for re-applying code ref activations after a <A HREF="#item_load"><CODE>load()</CODE></A>
call without having to type the code ref twice.
<P>You can also specify the extension in a simple array ref like this:</P>
<PRE>
$net->extend([2,3,1]);
</PRE>
<P>Which will simply add more nodes if needed to set the number of nodes in each layer to their
respective elements. This works just like the respective new() constructor, above.</P>
<P>NOTE: Your net will probably require re-training after adding nodes.</P>
<P></P>
<DT><STRONG><A NAME="item_extend_layer">$net->extend_layer($layer,\%hash);</A></STRONG><BR>
<DD>
With this you can modify only one layer with its specifications in a hash refrence. This hash
refrence uses the same keys as for the last <A HREF="#item_new"><CODE>new()</CODE></A> constructor form, above.
<P>You can also specify just the number of nodes for the layer in this form:</P>
<PRE>
$net->extend_layer(0,5);</PRE>
<P>Which will set the number of nodes in layer 0 to 5 nodes. This is the same as calling:
</P>
<PRE>
$net->add_nodes(0,5);</PRE>
<P>Which does the exact same thing. See <A HREF="#item_add_nodes"><CODE>add_nodes()</CODE></A> below.</P>
<P>NOTE: Your net will probably require re-training after adding nodes.</P>
<P></P>
<DT><STRONG><A NAME="item_add_nodes">$net->add_nodes($layer,$total_nodes);</A></STRONG><BR>
<DD>
This method was created mainly to service the extend*() group of functions, but it
can also be called independently. This will add nodes as needed to layer <CODE>$layer</CODE> to
make the nodes in layer equal to $total_nodes.
<P>NOTE: Your net will probably require re-training after adding nodes.</P>
<P></P>
in the network to STDIO.
<P></P>
<DT><STRONG><A NAME="item_crunch">$net->crunch($string);</A></STRONG><BR>
<DD>
This splits a string passed with /[\s\t]/ into an array ref containing unique indexes
to the words. The words are stored in an intenal array and preserved across <A HREF="#item_load"><CODE>load()</CODE></A> and <A HREF="#item_save"><CODE>save()</CODE></A>
calls. This is designed to be used to generate unique maps sutible for passing to <A HREF="#item_learn"><CODE>learn()</CODE></A> and
<A HREF="#item_run"><CODE>run()</CODE></A> directly. It returns an array ref.
<P>The words are not duplicated internally. For example:</P>
<PRE>
$net->crunch("How are you?");</PRE>
<P>Will probably return an array ref containing 1,2,3. A subsequent call of:</P>
<PRE>
$net->crunch("How is Jane?");</PRE>
<P>Will probably return an array ref containing 1,4,5. Notice, the first element stayed
the same. That is because it already stored the word ``How''. So, each word is stored
only once internally and the returned array ref reflects that.</P>
<P></P>
<DT><STRONG><A NAME="item_uncrunch">$net->uncrunch($array_ref);</A></STRONG><BR>
<DD>
Uncrunches a map (array ref) into an scalar string of words seperated by ' ' and returns the
string. This is ment to be used as a counterpart to the <A HREF="#item_crunch"><CODE>crunch()</CODE></A> method, above, possibly to
<A HREF="#item_uncrunch"><CODE>uncrunch()</CODE></A> the output of a <A HREF="#item_run"><CODE>run()</CODE></A> call. Consider the below code (also in ./examples/ex1.pl):
<PRE>
use AI::NeuralNet::Mesh;
my $net = AI::NeuralNet::Mesh->new(2,3);
for (0..3) {
$net->learn_set([
$net->crunch("I love chips."), $net->crunch("That's Junk Food!")),
$net->crunch("I love apples."), $net->crunch("Good, Healthy Food.")),
$net->crunch("I love pop."), $net->crunch("That's Junk Food!")),
$net->crunch("I love oranges."),$net->crunch("Good, Healthy Food."))
]);
}
print $net->run_uc("I love corn.")),"\n";</PRE>
<P>On my system, this responds with, ``Good, Healthy Food.'' If you try to run <A HREF="#item_crunch"><CODE>crunch()</CODE></A> with
``I love pop.'', though, you will probably get ``Food! apples. apples.'' (At least it returns
that on my system.) As you can see, the associations are not yet perfect, but it can make
for some interesting demos!</P>
<P></P>
<DT><STRONG><A NAME="item_crunched">$net->crunched($word);</A></STRONG><BR>
<DD>
This will return undef if the word is not in the internal crunch list, or it will return the
index of the word if it exists in the crunch list.
<P>If the word is not in the list, it will set the internal error value with a text message
<DT><STRONG>range(0..X);</STRONG><BR>
<DD>
<DT><STRONG>range(@range);</STRONG><BR>
<DD>
<DT><STRONG>range(A,B,C);</STRONG><BR>
<DD>
<A HREF="#item_range"><CODE>range()</CODE></A> returns a closure limiting the output
of that node to a specified set of values.
Good for use in output layers.
<P>Usage example:
$net->activation(4,range(0..5));
or (in the <A HREF="#item_new"><CODE>new()</CODE></A> hash constructor form):
..
{
nodes => 1,
activation => range 5..2
}
..
You can also pass an array containing the range
values (not array ref), or you can pass a comma-
seperated list of values as parameters:</P>
<PRE>
$net->activation(4,range(@numbers));
$net->activation(4,range(6,15,26,106,28,3));</PRE>
<P>Note: when using a <A HREF="#item_range"><CODE>range()</CODE></A> activatior, train the
net TWICE on the data set, because the first time
the <A HREF="#item_range"><CODE>range()</CODE></A> function searches for the top value in
the inputs, and therefore, results could flucuate.
The second learning cycle guarantees more accuracy.</P>
<P>The actual code that implements the range closure is
a bit convulted, so I will expand on it here as a simple
tutorial for custom activation functions.</P>
<PRE>
= line 1 = sub {
= line 2 = my @values = ( 6..10 );
= line 3 = my $sum = shift;
= line 4 = my $self = shift;
= line 5 = $self->{top_value}=$sum if($sum>$self->{top_value});
= line 6 = my $index = intr($sum/$self->{top_value}*$#values);
= line 7 = return $values[$index];
= line 8 = }</PRE>
<P>Now, the actual function fits in one line of code, but I expanded it a bit
here. Line 1 creates our array of allowed output values. Lines two and
three grab our parameters off the stack which allow us access to the
internals of this node. Line 5 checks to see if the sum output of this
node is higher than any previously encountered, and, if so, it sets
the marker higher. This also shows that you can use the $self refrence
to maintain information across activations. This technique is also used
in the <A HREF="#item_ramp"><CODE>ramp()</CODE></A> activator. Line 6 computes the index into the allowed
values array by first scaling the $sum to be between 0 and 1 and then
expanding it to fit smoothly inside the number of elements in the array. Then
access to the node just as if you were a blessed member of that node's object.</P>
<P></P>
<DT><STRONG><A NAME="item_ramp">ramp($r);</A></STRONG><BR>
<DD>
<A HREF="#item_ramp"><CODE>ramp()</CODE></A> preforms smooth ramp activation between 0 and 1 if $r is 1,
or between -1 and 1 if $r is 2. $r defaults to 1.
<P>You can get this into your namespace with the ':acts' export
tag as so:
</P>
<PRE>
use AI::NeuralNet::Mesh ':acts';</PRE>
<P>Note: when using a <A HREF="#item_ramp"><CODE>ramp()</CODE></A> activatior, train the
net at least TWICE on the data set, because the first
time the <A HREF="#item_ramp"><CODE>ramp()</CODE></A> function searches for the top value in
the inputs, and therefore, results could flucuate.
The second learning cycle guarantees more accuracy.</P>
<P>No code to show here, as it is almost exactly the same as range().</P>
<P></P>
<DT><STRONG><A NAME="item_and_gate">and_gate($threshold);</A></STRONG><BR>
<DD>
Self explanitory, pretty much. This turns the node into a basic AND gate.
$threshold is used to decide if an input is true or false (1 or 0). If
an input is below $threshold, it is false. $threshold defaults to 0.5.
<P>You can get this into your namespace with the ':acts' export
tag as so:
</P>
<PRE>
use AI::NeuralNet::Mesh ':acts';</PRE>
<P>Let's look at the code real quick, as it shows how to get at the indivudal
input connections:</P>
<PRE>
= line 1 = sub {
= line 2 = my $sum = shift;
= line 3 = my $self = shift;
= line 4 = my $threshold = 0.50;
= line 5 = for my $x (0..$self->{_inputs_size}-1) {
= line 6 = return 0.000001 if(!$self->{_inputs}->[$x]->{value}<$threshold)
= line 7 = }
= line 8 = return $sum/$self->{_inputs_size};
= line 9 = }</PRE>
<P>Line 2 and 3 pulls in our sum and self refrence. Line 5 opens a loop to go over
all the input lines into this node. Line 6 looks at each input line's value
and comparse it to the threshold. If the value of that line is below threshold, then
we return 0.000001 to signify a 0 value. (We don't return a 0 value so that the network
doen't get hung trying to multiply a 0 by a huge weight during training [it just will
keep getting a 0 as the product, and it will never learn]). Line 8 returns the mean
value of all the inputs if all inputs were above threshold.</P>
<P>Very simple, eh? :)
</P>
<P></P>
<DT><STRONG><A NAME="item_or_gate">or_gate($threshold);</A></STRONG><BR>
<DD>
<P>Self explanitory. Turns the node into a basic OR gate, $threshold is used same as above.</P>
<P>You can get this into your namespace with the ':acts' export
tag as so:
</P>
<PRE>
use AI::NeuralNet::Mesh ':acts';</PRE>
<P></P></DL>
<P>
<HR>
<H1><A NAME="variables">VARIABLES</A></H1>
<DL>
<DT><STRONG><A NAME="item_%24AI%3A%3ANeuralNet%3A%3AMesh%3A%3AConnector">$AI::NeuralNet::Mesh::Connector</A></STRONG><BR>
<DD>
This is an option is step up from average use of this module. This variable
should hold the fully qualified name of the function used to make the actual connections
between the nodes in the network. This contains '_c' by default, but if you use
this variable, be sure to add the fully qualified name of the method. For example,
in the ALN example, I use a connector in the main package called <CODE>tree()</CODE> instead of
the default connector. Before I call the <A HREF="#item_new"><CODE>new()</CODE></A> constructor, I use this line of code:
<PRE>
$AI::NeuralNet::Mesh::Connector = 'main::tree'
</PRE>
<P>The tree() function is called as a blessed method when it is used internally, providing
access to the bless refrence in the first argument. See notes on CUSTOM NETWORK CONNECTORS,
below, for more information on creating your own custom connector.</P>
<P></P>
<DT><STRONG><A NAME="item_%24AI%3A%3ANeuralNet%3A%3AMesh%3A%3ADEBUG">$AI::NeuralNet::Mesh::DEBUG</A></STRONG><BR>
<DD>
This variable controls the verbosity level. It will not hurt anything to set this
directly, yet most people find it easier to set it using the <A HREF="#item_debug"><CODE>debug()</CODE></A> method, or
any of its aliases.
<P>Creating custom network connectors is step up from average use of this module.
However, it can be very useful in creating other styles of neural networks, other
than the default fully-connected feed-foward network.</P>
<P>You create a custom connector by setting the variable $AI::NeuralNet::Mesh::Connector
to the fully qualified name of the function used to make the actual connections
between the nodes in the network. This variable contains '_c' by default, but if you use
this variable, be sure to add the fully qualified name of the method. For example,
in the ALN example, I use a connector in the main package called <CODE>tree()</CODE> instead of
the default connector. Before I call the <A HREF="#item_new"><CODE>new()</CODE></A> constructor, I use this line of code:</P>
<PRE>
$AI::NeuralNet::Mesh::Connector = 'main::tree'
</PRE>
<P>The tree() function is called as a blessed method when it is used internally, providing
access to the bless refrence in the first argument.</P>
<P>Example connector:</P>
<PRE>
sub connect_three {
my $self = shift;
my $r1a = shift;
my $r1b = shift;
my $r2a = shift;
my $r2b = shift;
my $mesh = $self->{mesh};
for my $y (0..($r1b-$r1a)-1) {
$mesh->[$y+$r1a]->add_output_node($mesh->[$y+$r2a-1]) if($y>0);
$mesh->[$y+$r1a]->add_output_node($mesh->[$y+$r2a]) if($y<($r2b-$r2a));
$mesh->[$y+$r1a]->add_output_node($mesh->[$y+$r2a+1]) if($y<($r2b-$r2a));
}
}</PRE>
<P>This is a very simple example. It feeds the outputs of every node in the first layer
to the node directly above it, as well as the nodes on either side of the node directly
above it, checking for range sides, of course.</P>
<P>The network is stored internally as one long array of node objects. The goal here
is to connect one range of nodes in that array to another range of nodes. The calling
function has already calculated the indices into the array, and it passed it to you
as the four arguments after the $self refrence. The first two arguments we will call
$r1a and $r1b. These define the start and end indices of the first range, or ``layer.'' Likewise,
the next two arguemnts, $r2a and $r2b, define the start and end indices of the second
layer. We also grab a refrence to the mesh array so we dont have to type the $self
part in a minute.) By adding or subtracting from this number we get the neighbor nodes.
In the above example you can see we check the $y index to see that we havn't come close to
any of the edges of the range.</P>
<P>Using $y+$r2a we get the index of the node to pass to <CODE>add_output_node()</CODE> on the first node at
$y+<STRONG>$r1a</STRONG>.</P>
<P>And that's all there is to it!</P>
<P>For the fun of it, we'll take a quick look at the default connector.
Below is the actual default connector code, albeit a bit cleaned up, as well as
line numbers added.</P>
<PRE>
= line 1 = sub _c {
= line 2 = my $self = shift;
= line 3 = my $r1a = shift;
= line 4 = my $r1b = shift;
= line 5 = my $r2a = shift;
= line 6 = my $r2b = shift;
= line 7 = my $mesh = $self->{mesh};
= line 8 = for my $y ($r1a..$r1b-1) {
= line 9 = for my $z ($r2a..$r2b-1) {
= line 10 = $mesh->[$y]->add_output_node($mesh->[$z]);
= line 11 = }
= line 12 = }
= line 12 = }
</PRE>
<P>Its that easy! The simplest connector (well almost anyways). It just connects each
node in the first layer defined by ($r1a..$r1b) to every node in the second layer as
defined by ($r2a..$r2b).</P>
<P>Those of you that are still reading, if you do come up with any new connection functions,
PLEASE SEND THEM TO ME. I would love to see what others are doing, as well as get new
network ideas. I will probably include any connectors you send over in future releases (with
propoer credit and permission, of course).</P>
<P>Anyways, happy coding!</P>
<P>
<P>Josiah Bryan <EM><<A HREF="mailto:jdb@wcoil.com">jdb@wcoil.com</A>></EM></P>
<P>Copyright (c) 2000 Josiah Bryan. All rights reserved. This program is free software;
you can redistribute it and/or modify it under the same terms as Perl itself.</P>
<P>The <CODE>AI::NeuralNet::Mesh</CODE> and related modules are free software. THEY COME WITHOUT WARRANTY OF ANY KIND.</P>
<P>$Id: AI::NeuralNet::Mesh.pm, v0.43 2000/15/09 03:29:08 josiah Exp $</P>
<P>
<HR>
<H1><A NAME="thanks">THANKS</A></H1>
<P>Below are a list of the people that have contributed in some way to this module (no particular order):</P>
<PRE>
Rodin Porrata, rodin@ursa.llnl.gov
Randal L. Schwartz, merlyn@stonehedge.com
Michiel de Roo, michiel@geo.uu.nl
</PRE>
<PRE>
Thanks to Randal and Michiel for spoting some documentation and makefile bugs in the last release.
Thanks to Rodin for continual suggetions and questions about the module and more.</PRE>
<P>
<HR>
<H1><A NAME="download">DOWNLOAD</A></H1>
<P>You can always download the latest copy of AI::NeuralNet::Mesh
from <A HREF="http://www.josiah.countystart.com/modules/get.pl?mesh:pod">http://www.josiah.countystart.com/modules/get.pl?mesh:pod</A></P>
<P>
<HR>
<H1><A NAME="mailing list">MAILING LIST</A></H1>
<P>A mailing list has been setup for AI::NeuralNet::Mesh and AI::NeuralNet::BackProp.
The list is for discussion of AI and neural net related topics as they pertain to
AI::NeuralNet::BackProp and AI::NeuralNet::mesh. I will also announce in the group
each time a new release of AI::NeuralNet::Mesh is available.</P>
The list address is: <A HREF="mailto:ai-neuralnet-backprop@egroups.com">ai-neuralnet-backprop@egroups.com</A> <BR>
To subscribe, send a blank email to: <A HREF="mailto:ai-neuralnet-backprop-subscribe@egroups.com">ai-neuralnet-backprop-subscribe@egroups.com</A>
<BR><BR><BR>
<HR>
<A HREF="http://www.josiah.countystart.com/modules/get.pl?mesh:(c)"><B>AI::NeuralNet::Mesh</B></A> - An optimized, accurate neural network Mesh. By <A HREF="mailto:jdb@wcoil.com"><B>Josiah Bryan</B></A>.
</BODY>
</HTML>
# Before `make install' is performed this script should be runnable with
# `make test'. After `make install' it should work as `perl test.pl'
BEGIN { $| = 1; print "1..13\n"; }
END {print "not ok 1\n" unless $loaded;}
sub t { my $f=shift;$t++;my $str=($f)?"ok $t":"not ok $t";print $str,"\n";}
use AI::NeuralNet::Mesh;
$loaded = 1;
t 1;
my $net = new AI::NeuralNet::Mesh(2,2,1);
t $net;
t ($net->intr(0.51) eq 1);
t ($net->intr(0.00001) eq 0);
t ($net->intr(0.50001) eq 1);
t $net->learn_set([
[ 1, 1 ], [ 2 ] ,
[ 1, 2 ], [ 3 ],
[ 2, 2 ], [ 4 ],
[ 20, 20 ], [ 40 ],
[ 100, 100 ], [ 200 ],
[ 150, 150 ], [ 300 ],
[ 500, 500 ], [ 1000 ],
],degrade=>1);
t ($net->run([60,40])->[0] eq 100);
t $net->save("add.mesh");
t (my $net2 = AI::NeuralNet::Mesh->new("add.mesh"));
t ($net2->run([60,40])->[0] eq 100);
t $net2->save("add.mesh");
t (-f "add.mesh");
t unlink("add.mesh");
( run in 0.497 second using v1.01-cache-2.11-cpan-4d50c553e7e )