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

NAME

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

SYNOPSIS

        $_ = AI::NeuralNet::Kohonen->new(
                map_dim_x => 39,
                map_dim_y => 19,
                epochs    => 100,
                table     =>
        "3
        1 0 0 red
        0 1 0 yellow
        0 0 1 blue
        0 1 1 cyan
        1 1 0 yellow
        1 .5 0 orange
        1 .5 1 pink"
        );
        $_->train;
        $_->save_file('mydata.txt');
        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 is illustrative....

Have a look at the AI::NeuralNet::Kohonen::Demo::RGB manpage for an example of visualisation of the map.

I'll maybe add some more text here later.

DEPENDENCIES

        AI::NeuralNet::Kohonen::Node
        AI::NeuralNet::Kohonen::Input

EXPORTS

None

CONSTRUCTOR new

Instantiates object fields:

input_file
A SOM_PAK training file to load. This does not prevent other input methods (input, table) being processed, but it does over-ride any specifications (weight_dim) which may have been explicitly handed to the constructor.

See also FILE FORMAT and METHOD load_input.

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
The contents of a file of the format that could be supplied to the input_file field.

input_names
A name for each dimension of the input vectors.

map_dim_x
map_dim_y
The dimensions of the feature map to create - defaults to a toy 19. (note: this is Perl indexing, starting at zero).

epochs
Number of epochs to run for (see METHOD train). Minimum number is 1.

learning_rate
The initial learning rate.

train_start
Reference to code to call at the begining of training.

epoch_start
Reference to code to call at the begining of every epoch (such as a colour calibration routine).

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.

targeting
If undefined, random targets are chosen; otherwise they're iterated over. Just for experimental purposes.

smoothing
The amount of smoothing to apply by default when smooth is applied (see METHOD smooth).

neighbour_factor
When working out the size of the neighbourhood of influence, the average of the dimensions of the map are divided by this variable, before the exponential function is applied: the default value is 2.5, but you may with to use 2 or 4.

missing_mask
Used to signify data is missing in an input vector. Defaults to x.

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.

map_dim_a
Average of the map dimensions.

METHOD randomise_map

Populates the map with nodes that contain random real nubmers.

See CONSTRUCTOR new in the AI::NerualNet::Kohonen::Node manpage.

METHOD clear_map

As METHOD randomise_map but sets all map nodes to either the value supplied as the only paramter, or undef.

METHOD train

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

An epoch is composed of A number of generations, the number being the total number of input vectors.

For every generation, iterates:

  1. selects a target from the input array (see PRIVATE METHOD _select_target);

  2. finds the best-matching unit (see METHOD find_bmu);

  3. adjusts the neighbours of the BMU (see PRIVATE METHOD _adjust_neighbours_of);

At the end of every generation, the learning rate is decayed (see PRIVATE METHOD _decay_learning_rate).

See CONSTRUCTOR new for details of applicable callbacks.

Returns a true value.

METHOD find_bmu

For a specific taraget, finds 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 (and should perhaps be abstracted as an object in its own right), indexed as follows:

  1. euclidean distance from the supplied target

  2. , 2
    x and y co-ordinate in the map

See METHOD get_weight_at, and distance_from in the AI::NeuralNet::Kohonen::Node manpage,

METHOD get_weight_at

Returns a reference to the weight array at the supplied x,y co-ordinates.

Accepts: x,y co-ordinates, each a scalar.

Returns: reference to an array that is the weight of the node, or undef on failure.

METHOD get_results

Finds and returns the results for all input vectors in the supplied reference to an array of arrays, placing the values in the results field (array reference), and, returning it either as an array or as it is, depending on the calling context

If no array reference of input vectors is supplied, will use the values in the input field.

Individual results are in the array format as described in METHOD find_bmu.

See METHOD find_bmu, and METHOD get_weight_at.

METHOD map_results

Clears the map and fills it with the results.

The sole paramter is passed to the METHOD clear_map. METHOD get_results is then called, and the results returned fed into the object field map.

This may change, as it seems misleading to re-use that field.

METHOD dump

Print the current weight values to the screen.

METHOD smooth

Perform gaussian smoothing upon the map.

Accepts: the length of the side of the square gaussian mask to apply. If not supplied, uses the value in the field smoothing; if that is empty, uses the square root of the average of the map dimensions (map_dim_a).

Returns: a true value.

METHOD load_input

Loads a SOM_PAK-format file of input vectors.

This method is automatically accessed if the constructor is supplied with an input_file field.

Requires: a path to a file.

Returns undef on failure.

See FILE FORMAT.

METHOD save_file

Saves the map file in SOM_PAK format (see METHOD load_input) at the path specified in the first argument.

Return undef on failure, a true value on success.

PRIVATE METHOD _select_target

Return a random target from the training set in the input field, unless the targeting field is defined, when the targets are iterated over.

PRIVATE METHOD _adjust_neighbours_of

Accepts: a reference to an array containing the distance of the BMU from the target, as well as the x and y co-ordinates of the BMU in the map; a reference to the target, which is an AI::NeuralNet::Kohonen::Input object.

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 the AI::NeuralNet::Kohonen::Node manpage.

PRIVATE METHOD _decay_learning_rate

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

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

PRIVATE FUNCTION _make_gaussian_mask

Accepts: size of mask.

Returns: reference to a 2d array that is the mask.

PRIVATE FUNCTION _gauss_weight

Accepts: two paramters: the first, r, gives the distance from the mask centre, the second, sigma, specifies the width of the mask.

Returns the gaussian weight.

See also _decay_learning_rate.

PUBLIC METHOD quantise_error

Returns the quantise error for either the supplied points, or those in the input field.

PRIVATE METHOD _add_input_from_str

Adds to the input field an input vector in SOM_PAK-format whitespace-delimited ASCII.

Returns undef on failure to add an item (perhaps because the data passed was a comment, or the weight_dim flag was not set); a true value on success.

FILE FORMAT

This module has begun to attempt the SOM_PAK format: SOM_PAK file format version 3.1 (April 7, 1995), Helsinki University of Technology, Espoo:

The input data is stored in ASCII-form as a list of entries, one line ...for each vectorial sample.

The first line of the file is reserved for status knowledge of the entries; in the present version it is used to define the following items (these items MUST occur in the indicated order):

   - Dimensionality of the vectors (integer, compulsory).
   - Topology type, either hexa or rect (string, optional, case-sensitive).
   - Map dimension in x-direction (integer, optional).
   - Map dimension in y-direction (integer, optional).
   - Neighborhood type, either bubble or gaussian (string, optional, case-sen-
      sitive).

...

Subsequent lines consist of n floating-point numbers followed by an optional class label (that can be any string) and two optional qualifiers (see below) that determine the usage of the corresponding data entry in training programs. The data files can also contain an arbitrary number of comment lines that begin with '#', and are ignored. (One '#' for each comment line is needed.)

If some components of some data vectors are missing (due to data collection failures or any other reason) those components should be marked with 'x'...[in processing, these] are ignored.

...

Each data line may have two optional qualifiers that determine the usage of the data entry during training. The qualifiers are of the form codeword=value, where spaces are not allowed between the parts of the qualifier. The optional qualifiers are the following:

-
Enhancement factor: e.g. weight=3. The training rate for the corresponding input pattern vector is multiplied by this parameter so that the reference vectors are updated as if this input vector were repeated 3 times during training (i.e., as if the same vector had been stored 2 extra times in the data file).

-
Fixed-point qualifier: e.g. fixed=2,5. The map unit defined by the fixed-point coordinates (x = 2; y = 5) is selected instead of the best-matching unit for training. (See below for the definition of coordinates over the map.) If several inputs are forced to known locations, a wanted orientation results in the map.

Not (yet) implimented in file format:

SEE ALSO

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

The documentation for SOM_PAK, which has lots of advice on map building that may or may not be applicable yet.

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

AUTHOR AND COYRIGHT

This implimentation Copyright (C) Lee Goddard, 2003-2006. All Rights Reserved.

Available under the same terms as Perl itself.

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