/ 
Kohonen-SOM-0.1
/ AI::NeuralNet::Kohonen

NAME

AI::NeuralNet::Kohonen - Kohonen's Self-organising Maps

SYNOPSIS

$_ = AI::NeuralNet::Kohonen->new(
	map_dim	=> 39,
	epochs => 100,
	table=>
"R G B
1 0 0
0 1 0
0 0 1
1 1 0
1 0 1
0 1 1
1 1 1
");

$_->dump;
$_->tk_dump;

$_->train;

$_->dump;
$_->tk_dump;
exit;

DESCRIPTION

An illustrative implimentation of Kohonen's Self-organising Feature Maps (SOMs) in Perl.

It's not fast - it's illustrative.

In fact, it's slow: but it's illustrative....

Have a look at AI::NeuralNet::Kohonen::Demo::RGB.

I'll add some more text here later.

CONSTRUCTOR new

Sets up object fields:

input

A reference to an array of training vectors, within which each vector is represented by an array:

[ [v1a, v1b, v1c], [v2a,v2b,v2c], ..., [vNa,vNb,vNc] ]

See also table.

table

A scalar that is a table, lines delimited by [\r\f\n]+, columns by whitespace, initial whitespace stripped. First line should be column names, the following lines should be just data. See also input.

input_names

A name for each dimension of the input vectors.

map_dim

The size of one dimension of the feature map to create - defaults to a toy 19. (note: this is Perl indexing).

epochs

Number of epochs to run for (see "METHOD train").

learning_rate

The initial learning rate.

train_start

Reference to code to call at the begining of training.

epoch_end

Reference to code to call at the end of every epoch (such as a display routine).

train_end

Reference to code to call at the end of training.

Private fields:

time_constant

The number of iterations (epochs) to be completed, over the log of the map radius.

t

The current epoch, or moment in time.

l

The current learning rate.

METHOD train

Optionally accepts a parameter that is the number of epochs to train for - default is the value in the epochs field.

For every epoch, iterates:

- selects a random target from the input array;
- finds the best bmu
- adjusts neighbours of the bmu
- decays the learning rate

METHOD dump

Print the current weight values to the screen.

METHOD tk_dump;

Dumps the weights to a TK screen.

PRIVATE METHOD _select_target

Return a random target from the training set in the input field.

PRIVATE METHOD _find_bmu

Find the Best Matching Unit in the map and return the x/y index.

Accepts: a reference to an array that is the target.

Returns: a reference to an array that is the BMU, of the format

[euclidean-distance-from-target, our-x-co-ord, our-y-co-ord]

See "distance_from" in AI::NeuralNet::Kohonen::Node.

PRIVATE METHOD _adjust_neighbours_of

Accepts: a reference to an array containing the distance of the BMU from the target, and the x and y co-ordinates of the BMU in the map; a reference to an array that is the target.

Returns: true.

FINDING THE NEIGHBOURS OF THE BMU

                        (      t   )
sigma(t) = sigma(0) exp ( - ------ )
                        (   lambda )

Where sigma is the width of the map at any stage in time (t), and lambda is a time constant.

Lambda is our field time_constant.

The map radius is naturally just half the map width.

ADJUSTING THE NEIGHBOURS OF THE BMU

W(t+1) = W(t) + THETA(t) L(t)( V(t)-W(t) )

Where L is the learning rate, V the target vector, and W the weight. THETA(t) represents the influence of distance from the BMU upon a node's learning, and is calculated by the Node class - see "distance_effect" in AI::NeuralNet::Kohonen::Node.

PRIVATE METHOD _decay_learning_rate

Performs a gaussian decay upon the learning rate (our l field).

              (       t   )
L(t) = L  exp ( -  ------ )
        0     (    lambda )

SEE ALSO

See "distance_from" in AI::NeuralNet::Kohonen::Node; AI::NeuralNet::Kohonen::Demo::RGB.

A very nice explanation of Kohonen's algorithm: AI-Junkie SOM tutorial part 1

AUTHOR AND COYRIGHT

This implimentation Copyright (C) Lee Goddard, 2003. All Rights Reserved.

Available under the same terms as Perl itself.