AI-NeuralNet-Mesh
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<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>
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<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
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 <A HREF="#item_load_set"><CODE>load_set()</CODE></A> 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? :-)</P>
<P>
<HR>
<H1><A NAME="description">DESCRIPTION</A></H1>
<P>AI::NeuralNet::Mesh is an optimized, accurate neural network Mesh.
It was designed with accruacy and speed in mind.</P>
<P>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.</P>
<P>This module is designed to also be a customizable, extensable
neural network simulation toolkit. Through a combination of setting
the $Connection variable and using custom activation functions, as
well as basic package inheritance, you can simulate many different
types of neural network structures with very little new code written
by you.</P>
<P>In this module I have included a more accurate form of ``learning'' for the
mesh. This form preforms descent toward a local error minimum (0) on a
directional delta, rather than the desired value for that node. This allows
for better, and more accurate results with larger datasets. This module also
uses a simpler recursion technique which, suprisingly, is more accurate than
the original technique that I've used in other ANNs.</P>
<P>
<HR>
<H1><A NAME="exports">EXPORTS</A></H1>
<P>This module exports three functions by default:</P>
<PRE>
range
intr
pdiff
</PRE>
<P>See range() intr() and pdiff() for description of their respective functions.</P>
<P>Also provided are several export tag sets for usage in the form of:</P>
<PRE>
use AI::NeuralNet::Mesh ':tag';
</PRE>
<P>Tag sets are:</P>
<PRE>
:default
- These functions are always exported.
- Exports:
range()
intr()
pdiff()
:all
- Exports:
p()
high()
low()
range()
ramp()
and_gate()
or_gate()
:p
- Exports:
p()
high()
low()
:acts
- Exports:
ramp()
and_gate()
or_gate()
</PRE>
<P>See the respective methods/functions for information about
each method/functions usage.</P>
<P>
<HR>
<H1><A NAME="methods">METHODS</A></H1>
<DL>
<DT><STRONG><A NAME="item_new">AI::NeuralNet::Mesh->new();</A></STRONG><BR>
<DD>
There are four ways to construct a new network with new(). Each is detailed below.
<P>P.S. Don't worry, the old <A HREF="#item_new"><CODE>new($layers, $nodes [, $outputs])</CODE></A> still works like always!</P>
<P></P>
<DT><STRONG>AI::NeuralNet::Mesh->new($layers, $nodes [, $outputs]);</STRONG><BR>
<DD>
<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, $self);
</PRE>
<P>The code ref is expected to return a value to be used as the output of the node.
The code ref also has access to all the data of that node through the second argument,
a blessed hash refrence to that node.</P>
<P>See CUSTOM ACTIVATION FUNCTIONS for information on several included activation functions
other than the ones listed above.</P>
<P>Three of the activation syntaxes are shown in the first constructor above, the ``linear'',
``sigmoid'' and code ref types.</P>
<P>You can also set the activation and threshold values after network creation with the
<A HREF="#item_activation"><CODE>activation()</CODE></A> and <A HREF="#item_threshold"><CODE>threshold()</CODE></A> methods.</P>
<P></P>
<P></P>
<DT><STRONG><A NAME="item_learn">$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,
then <A HREF="#item_learn"><CODE>learn()</CODE></A> will not return until it gets an exact match for the desired result OR it
reaches $maximum_iterations.</P>
<P>$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.</P>
<P>In previous module releases $degrade_increment_flag was not used, as increment degrading
was always on. In this release I have looked at several other network types as well
as several texts and decided that it would be better to not use increment degrading. The
option is still there for those that feel the inclination to use it. I have found some areas
that do need the degrade flag to work at a faster speed. See test.pl for an example. If
the degrade flag wasn't in test.pl, it would take a very long time to learn.</P>
<P></P>
<DT><STRONG><A NAME="item_learn_set">$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>
Simple utility function which takes an array ref of the same structure as the <A HREF="#item_learn_set"><CODE>learn_set()</CODE></A> method,
above. It returns an array ref of the same type as <A HREF="#item_run_set"><CODE>run_set()</CODE></A> wherein each element contains an
output value. The output values are the target values specified in the $set passed. Each element
in the returned array ref represents the output value for the corrseponding row in the dataset
passed. (A row is two elements of the dataset together, see <A HREF="#item_learn_set"><CODE>learn_set()</CODE></A> for dataset structure.)
<P></P>
<DT><STRONG><A NAME="item_load_set">$net->load_set($file,$column,$seperator);</A></STRONG><BR>
<DD>
Loads a CSV-like dataset from disk
<P>Returns a data set of the same structure as required by the
<A HREF="#item_learn_set"><CODE>learn_set()</CODE></A> 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. $seperator defaults to ',' (a single comma).
NOTE: This does not handle quoted fields, or any other record
seperator other than ``\n''.</P>
<P>The returned array ref is suitable for passing directly to
<A HREF="#item_learn_set"><CODE>learn_set()</CODE></A> or get_outs().</P>
<P></P>
<DT><STRONG><A NAME="item_range">$net->range();</A></STRONG><BR>
<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>Toggles debugging off if called with $level = 0 or no arguments. There are several levels
of debugging.</P>
<P>NOTE: Debugging verbosity has been toned down somewhat from AI::NeuralNet::BackProp,
but level 4 still prints the same amount of information as you were used to. The other
levels, however, are mostly for advanced use. Not much explanation in the other
levels, but they are included for those of you that feel daring (or just plain bored.)</P>
<P>Level 0 ($level = 0) : Default, no debugging information printed. All printing is
left to calling script.</P>
<P>Level 1 ($level = 1) : Displays the activity between nodes, prints what values were
received and what they were weighted to.</P>
<P>Level 2 ($level = 2) : Just prints info from the <A HREF="#item_learn"><CODE>learn()</CODE></A> 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.</P>
<P>Level 3 ($level = 3) : I don't think I included any level 3 debugs in this version.</P>
<P>Level 4 ($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.</P>
<P>Level 12 ($level = 12) : Level 12 prints a dot (period) [.] after each learning loop is
complete. This is useful for letting the user know that stuff is happening, but without
having to display any of the internal variables. I use this in the ex_aln.pl demo,
as well as the ex_agents.pl demo.</P>
<P>Toggles debuging off when called with no arguments.</P>
<P></P>
<DT><STRONG><A NAME="item_save">$net->save($filename);</A></STRONG><BR>
<DD>
This will save the complete state of the network to disk, including all weights and any
words crunched with <A HREF="#item_crunch"><CODE>crunch()</CODE></A> . Also saves the layer size and activations of the network.
<P>NOTE: The only activation type NOT saved is the CODE ref type, which must be set again
after loading.</P>
<P>This uses a simple flat-file text storage format, and therefore the network files should
be fairly portable.</P>
<P>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 <A HREF="#item_error"><CODE>error()</CODE></A> method,
below.</P>
<P>If there were no errors, it will return a refrence to $net.</P>
<P></P>
<DT><STRONG><A NAME="item_load">$net->load($filename);</A></STRONG><BR>
<DD>
This will load from disk any network saved by <A HREF="#item_save"><CODE>save()</CODE></A> and completly restore the internal
state at the point it was <A HREF="#item_save"><CODE>save()</CODE></A> was called at.
<P>If the file is of an invalid file type, then <A HREF="#item_load"><CODE>load()</CODE></A> will
return undef. Use the <A HREF="#item_error"><CODE>error()</CODE></A> method, below, to print the error message.</P>
<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, $self);
</PRE>
<P>The code ref is expected to return a value to be used as the output of the node.
The code ref also has access to all the data of that node through the second argument,
a blessed hash refrence to that node.</P>
<P>See CUSTOM ACTIVATION FUNCTIONS for information on several included activation functions
other than the ones listed above.</P>
<P>The activation type for each layer is preserved across load/save calls.</P>
<P>EXCEPTION: Due to the constraints of Perl, I cannot load/save the actual subs that the code
ref option points to. Therefore, you must re-apply any code ref activation types after a
<A HREF="#item_load"><CODE>load()</CODE></A> call.</P>
<P></P>
<DT><STRONG><A NAME="item_node_activation">$net->node_activation($layer,$node,$type);</A></STRONG><BR>
<DD>
This sets the activation function for a specific node in a layer. The same notes apply
here as to the <A HREF="#item_activation"><CODE>activation()</CODE></A> method above.
<P></P>
<DT><STRONG><A NAME="item_threshold">$net->threshold($layer,$value);</A></STRONG><BR>
<DD>
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''.
<P></P>
<DT><STRONG><A NAME="item_node_threshold">$net->node_threshold($layer,$node,$value);</A></STRONG><BR>
<DD>
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''.
<P></P>
<DT><STRONG><A NAME="item_join_cols">$net->join_cols($array_ref,$row_length_in_elements,$high_state_character,$low_state_character);</A></STRONG><BR>
<DD>
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 <CODE>join()</CODE> ,
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 $high_state_character is a null or empty or
undefined string, it <A HREF="#item_join_cols"><CODE>join_cols()</CODE></A> will just print the numerical value of each element seperated
by a null character (\0). <A HREF="#item_join_cols"><CODE>join_cols()</CODE></A> defaults to the latter behaviour.
<P></P>
<DT><STRONG><A NAME="item_extend">$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>
$net->add_nodes(0,5);</PRE>
<P>Which does the exact same thing. See <A HREF="#item_add_nodes"><CODE>add_nodes()</CODE></A> below.</P>
to every input line when a set of inputs are <A HREF="#item_run"><CODE>run()</CODE></A> or <A HREF="#item_learn"><CODE>learn()</CODE></A> -ed, to prevent the
network from hanging on a 0 value. When called with no arguments, it returns the current
const. value. It defaults to 0.0001 on a newly-created network. The run const. value
is preserved across <A HREF="#item_load"><CODE>load()</CODE></A> and <A HREF="#item_save"><CODE>save()</CODE></A> calls.
<P></P>
<DT><STRONG><A NAME="item_error">$net->error();</A></STRONG><BR>
<DD>
Returns the last error message which occured in the mesh, or undef if no errors have
occured.
<P></P>
<DT><STRONG><A NAME="item_load_pcx">$net->load_pcx($filename);</A></STRONG><BR>
<DD>
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 <A HREF="#item_error"><CODE>error()</CODE></A> method, below.
<P>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.</P>
<P>See <CODE>perldoc PCX::Loader</CODE> for information on the methods of the object returned.</P>
<P>You can download PCX::Loader from <A HREF="http://www.josiah.countystart.com/modules/get.pl?pcx-loader:mpod">http://www.josiah.countystart.com/modules/get.pl?pcx-loader:mpod</A></P>
<P></P></DL>
<P>
<HR>
<H1><A NAME="custom activation functions">CUSTOM ACTIVATION FUNCTIONS</A></H1>
<P>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 <A HREF="#item_range"><CODE>range()</CODE></A> 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.</P>
<DL>
<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 $sum to be between 0 and 1 and then
expanding it to fit smoothly inside the number of elements in the array. Then
we simply round to an integer and pluck that index from the array and
use it as the output value for that node.</P>
<P>See? It's not that hard! Using custom activation functions, you could do
just about anything with the node that you want to, since you have
access to the node just as if you were a blessed member of that node's object.</P>
<P></P>
<DT><STRONG><A NAME="item_ramp">ramp($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>
$AI::NeuralNet::Mesh::Connector = 'main::tree'
<P>$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.</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>
<HR>
<H1><A NAME="what can it do">WHAT CAN IT DO?</A></H1>
<P>Rodin Porrata asked on the ai-neuralnet-backprop malining list,
``What can they [Neural Networks] do?''. In regards to that questioin,
consider the following:</P>
<P>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.</P>
<P>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.</P>
<P>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.</P>
<P>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.</P>
<P>In short, Neural Networks are poor at precise calculations, but good at
association, evaluation, and pattern recognition.</P>
<P>
<HR>
<H1><A NAME="examples">EXAMPLES</A></H1>
<P>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.</P>
<P>
<HR>
<H1><A NAME="other included packages">OTHER INCLUDED PACKAGES</A></H1>
<P>These packages are not designed to be called directly, they are for internal use. They are
listed here simply for your refrence.</P>
<DL>
<DT><STRONG><A NAME="item_AI%3A%3ANeuralNet%3A%3AMesh%3A%3Anode">AI::NeuralNet::Mesh::node</A></STRONG><BR>
<DD>
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.
<P></P>
<DT><STRONG><A NAME="item_AI%3A%3ANeuralNet%3A%3AMesh%3A%3Acap">AI::NeuralNet::Mesh::cap</A></STRONG><BR>
<DD>
This is applied to the input layer of the mesh to prevent the mesh from trying to recursivly
adjust weights out throug the inputs.
<P></P>
<DT><STRONG><A NAME="item_AI%3A%3ANeuralNet%3A%3AMesh%3A%3Aoutput">AI::NeuralNet::Mesh::output</A></STRONG><BR>
<DD>
This is simply a data collector package clamped onto the output layer to record the data
as it comes out of the mesh.
<P></P></DL>
<P>
<HR>
<H1><A NAME="bugs">BUGS</A></H1>
<P>This is a beta release of <CODE>AI::NeuralNet::Mesh</CODE>, 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 <EM><<A HREF="mailto:jdb@wcoil.com">jdb@wcoil.com</A>></EM>,
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 <EM><<A HREF="mailto:jdb@wcoil.com">jdb@wcoil.com</A>></EM>.</P>
<P>
<HR>
<H1><A NAME="author">AUTHOR</A></H1>
<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>.
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