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lib/AI/NeuralNet/SOM.pm  view on Meta::CPAN

package AI::NeuralNet::SOM;

use strict;
use warnings;

require Exporter;
use base qw(Exporter);

use Data::Dumper;

=pod

=head1 NAME

AI::NeuralNet::SOM - Perl extension for Kohonen Maps

=head1 SYNOPSIS

  use AI::NeuralNet::SOM::Rect;
  my $nn = new AI::NeuralNet::SOM::Rect (output_dim => "5x6",
                                         input_dim  => 3);
  $nn->initialize;
  $nn->train (30, 
    [ 3, 2, 4 ], 
    [ -1, -1, -1 ],
    [ 0, 4, -3]);

  my @mes = $nn->train (30, ...);      # learn about the smallest errors
                                       # during training

  print $nn->as_data;                  # dump the raw data
  print $nn->as_string;                # prepare a somehow formatted string

  use AI::NeuralNet::SOM::Torus;
  # similar to above

  use AI::NeuralNet::SOM::Hexa;
  my $nn = new AI::NeuralNet::SOM::Hexa (output_dim => 6,
                                         input_dim  => 4);
  $nn->initialize ( [ 0, 0, 0, 0 ] );  # all get this value

  $nn->value (3, 2, [ 1, 1, 1, 1 ]);   # change value for a neuron
  print $nn->value (3, 2);

  $nn->label (3, 2, 'Danger');         # add a label to the neuron
  print $nn->label (3, 2);


=head1 DESCRIPTION

This package is a stripped down implementation of the Kohonen Maps
(self organizing maps). It is B<NOT> meant as demonstration or for use
together with some visualisation software. And while it is not (yet)
optimized for speed, some consideration has been given that it is not
overly slow.

Particular emphasis has been given that the package plays nicely with
others. So no use of files, no arcane dependencies, etc.

=head2 Scenario

The basic idea is that the neural network consists of a 2-dimensional
array of N-dimensional vectors. When the training is started these
vectors may be completely random, but over time the network learns
from the sample data, which is a set of N-dimensional vectors.

Slowly, the vectors in the network will try to approximate the sample
vectors fed in. If in the sample vectors there were clusters, then
these clusters will be neighbourhoods within the rectangle (or
whatever topology you are using).

Technically, you have reduced your dimension from N to 2.

=head1 INTERFACE

=head2 Constructor

The constructor takes arguments:

=over

=item C<input_dim> : (mandatory, no default)

A positive integer specifying the dimension of the sample vectors (and hence that of the vectors in
the grid).

=item C<learning_rate>: (optional, default C<0.1>)

This is a magic number which controls how strongly the vectors in the grid can be influenced. Stronger
movement can mean faster learning if the clusters are very pronounced. If not, then the movement is
like noise and the convergence is not good. To mediate that effect, the learning rate is reduced
over the iterations.

=item C<sigma0>: (optional, defaults to radius)

A non-negative number representing the start value for the learning radius. Practically, the value
should be chosen in such a way to cover a larger part of the map. During the learning process this
value will be narrowed down, so that the learning radius impacts less and less neurons.

B<NOTE>: Do not choose C<1> as the C<log> function is used on this value.

=back

Subclasses will (re)define some of these parameters and add others:

Example:

lib/AI/NeuralNet/SOM.pm  view on Meta::CPAN

Returns the I<radius> of the map. Different topologies interpret this differently.

=item I<map>

I<$m> = I<$nn>->map

This method returns a reference to the map data. See the appropriate subclass of the data
representation.

=cut

sub map {
    my $self = shift;
    return $self->{map};
}

=pod

=item I<value>

I<$val> = I<$nn>->value (I<$x>, I<$y>)

I<$nn>->value (I<$x>, I<$y>, I<$val>)

Set or get the current vector value for a particular neuron. The neuron is addressed via its
coordinates.

=cut

sub value {
    my $self    = shift;
    my ($x, $y) = (shift, shift);
    my $v       = shift;
    return defined $v ? $self->{map}->[$x]->[$y] = $v : $self->{map}->[$x]->[$y];
}

=pod

=item I<label>

I<$label> = I<$nn>->label (I<$x>, I<$y>)

I<$nn>->label (I<$x>, I<$y>, I<$label>)

Set or get the label for a particular neuron. The neuron is addressed via its coordinates.
The label can be anything, it is just attached to the position.

=cut

sub label {
    my $self    = shift;
    my ($x, $y) = (shift, shift);
    my $l       = shift;
    return defined $l ? $self->{labels}->[$x]->[$y] = $l : $self->{labels}->[$x]->[$y];
}

=pod

=item I<as_string>

print I<$nn>->as_string

This methods creates a pretty-print version of the current vectors.

=cut

sub as_string { die; }

=pod

=item I<as_data>

print I<$nn>->as_data

This methods creates a string containing the raw vector data, row by
row. This can be fed into gnuplot, for instance.

=cut

sub as_data { die; }

=pod

=back

=head1 HOWTOs

=over

=item I<using Eigenvectors to initialize the SOM>

See the example script in the directory C<examples> provided in the
distribution. It uses L<PDL> (for speed and scalability, but the
results are not as good as I had thought).

=item I<loading and saving a SOM>

See the example script in the directory C<examples>. It uses
C<Storable> to directly dump the data structure onto disk. Storage and
retrieval is quite fast.

=back

=head1 FAQs

=over

=item I<I get 'uninitialized value ...' warnings, many of them>

There is most likely something wrong with the C<input_dim> you
specified and your vectors should be having.

=back

=head1 TODOs

=over

=item maybe implement the SOM on top of PDL?

=item provide a ::SOM::Compat to have compatibility with the original AI::NeuralNet::SOM?

=item implement different window forms (bubble/gaussian), linear/random

=item implement the format mentioned in the original AI::NeuralNet::SOM

=item add methods as_html to individual topologies

=item add iterators through vector lists for I<initialize> and I<train>

=back

=head1 SUPPORT