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Steve Purkis

NAME

AI::Perceptron - example of a node in a neural network.

SYNOPSIS

`````` use AI::Perceptron;

my \$p = AI::Perceptron->new
->num_inputs( 2 )
->learning_rate( 0.04 )
->threshold( 0.02 )
->weights([ 0.1, 0.2 ]);

my @inputs  = ( 1.3, -0.45 );   # input can be any number
my \$target  = 1;                # output is always -1 or 1
my \$current = \$p->compute_output( @inputs );

print "current output: \$current, target: \$target\n";

\$p->add_examples( [ \$target, @inputs ] );

\$p->max_iterations( 10 )->train or
warn "couldn't train in 10 iterations!";

print "training until it gets it right\n";
\$p->max_iterations( -1 )->train; # watch out for infinite loops``````

DESCRIPTION

This module is meant to show how a single node of a neural network works.

Training is done by the Stochastic Approximation of the Gradient-Descent model.

MODEL

Model of a Perceptron

``````              +---------------+
X[1] o------ |W[1]      T    |
X[2] o------ |W[2] +---------+         +-------------------+
.           | .   |   ___   |_________|    __  Squarewave |_______\  Output
.           | .   |   \     |    S    | __|    Generator  |       /
.           | .   |   /__   |         +-------------------+
X[n] o------ |W[n] |   Sum   |
+-----+---------+

S  =  T + Sum( W[i]*X[i] )  as i goes from 1 -> n
Output  =  1 if S > 0; else -1``````

Where `X[n]` are the perceptron's inputs, `W[n]` are the Weights that get applied to the corresponding input, and `T` is the Threshold.

The squarewave generator just turns the result into a positive or negative number.

So in summary, when you feed the perceptron some numeric inputs you get either a positive or negative output depending on the input's weights and a threshold.

TRAINING

Usually you have to train a perceptron before it will give you the outputs you expect. This is done by giving the perceptron a set of examples containing the output you want for some given inputs:

``````    -1 => -1, -1
-1 =>  1, -1
-1 => -1,  1
1 =>  1,  1``````

If you've ever studied boolean logic, you should recognize that as the truth table for an `AND` gate (ok so we're using -1 instead of the commonly used 0, same thing really).

You train the perceptron by iterating over the examples and adjusting the weights and threshold by some value until the perceptron's output matches the expected output of each example:

``````    while some examples are incorrectly classified
update weights for each example that fails``````

The value each weight is adjusted by is calculated as follows:

``    delta[i] = learning_rate * (expected_output - output) * input[i]``

Which is know as a negative feedback loop - it uses the current output as an input to determine what the next output will be.

Also, note that this means you can get stuck in an infinite loop. It's not a bad idea to set the maximum number of iterations to prevent that.

CONSTRUCTOR

new( [%args] )

Creates a new perceptron with the following default properties:

``````    num_inputs    = 1
learning_rate = 0.01
threshold     = 0.0
weights       = empty list``````

Ideally you should use the accessors to set the properties, but for backwards compatability you can still use the following arguments:

``````    Inputs => \$number_of_inputs  (positive int)
N      => \$learning_rate     (float)
W      => [ @weights ]       (floats)``````

The number of elements in W must be equal to the number of inputs plus one. This is because older version of AI::Perceptron combined the threshold and the weights a single list where W[0] was the threshold and W[1] was the first weight. Great idea, eh? :) That's why it's DEPRECATED.

ACCESSORS

num_inputs( [ \$int ] )

Set/get the perceptron's number of inputs.

learning_rate( [ \$float ] )

Set/get the perceptron's number of inputs.

weights( [ \@weights ] )

Set/get the perceptron's weights (floats).

For backwards compatability, returns a list containing the threshold as the first element in list context:

``  (\$threshold, @weights) = \$p->weights;``

This usage is DEPRECATED.

threshold( [ \$float ] )

Set/get the perceptron's number of inputs.

training_examples( [ \@examples ] )

Set/get the perceptron's list of training examples. This should be a list of arrayrefs of the form:

``    [ \$expected_result => @inputs ]``
max_iterations( [ \$int ] )

Set/get the perceptron's number of inputs, a negative value implies no maximum.

METHODS

compute_output( @inputs )

Computes and returns the perceptron's output (either -1 or 1) for the given inputs. See the above model for more details.

Adds the @training_examples to to current list of examples. See training_examples() for more details.

train( [ @training_examples ] )

Uses the Stochastic Approximation of the Gradient-Descent model to adjust the perceptron's weights until all training examples are classified correctly.

@training_examples can be passed for convenience. These are passed to add_examples(). If you want to re-train the perceptron with an entirely new set of examples, reset the training_examples().

AUTHOR

Steve Purkis <spurkis@epn.nu>