# learnk

Kohonen weight learning function

## Syntax

[dW,LS] = learnk(W,P,Z,N,A,T,E,gW,gA,D,LP,LS)
info = learnk('code')

## Description

learnk is the Kohonen weight learning function.

[dW,LS] = learnk(W,P,Z,N,A,T,E,gW,gA,D,LP,LS) takes several inputs,

 W S-by-R weight matrix (or S-by-1 bias vector) P R-by-Q input vectors (or ones(1,Q)) Z S-by-Q weighted input vectors N S-by-Q net input vectors A S-by-Q output vectors T S-by-Q layer target vectors E S-by-Q layer error vectors gW S-by-R gradient with respect to performance gA S-by-Q output gradient with respect to performance D S-by-S neuron distances LP Learning parameters, none, LP = [] LS Learning state, initially should be = []

and returns

 dW S-by-R weight (or bias) change matrix LS New learning state

Learning occurs according to learnk’s learning parameter, shown here with its default value.

 LP.lr - 0.01 Learning rate

info = learnk('code') returns useful information for each code character vector:

 'pnames' Names of learning parameters 'pdefaults' Default learning parameters 'needg' Returns 1 if this function uses gW or gA

## Examples

Here you define a random input P, output A, and weight matrix W for a layer with a two-element input and three neurons. Also define the learning rate LR.

p = rand(2,1);
a = rand(3,1);
w = rand(3,2);
lp.lr = 0.5;

Because learnk only needs these values to calculate a weight change (see “Algorithm” below), use them to do so.

dW = learnk(w,p,[],[],a,[],[],[],[],[],lp,[])

## Network Use

To prepare the weights of layer i of a custom network to learn with learnk,

1. Set net.trainFcn to 'trainr'. (net.trainParam automatically becomes trainr’s default parameters.)

3. Set each net.inputWeights{i,j}.learnFcn to 'learnk'.

4. Set each net.layerWeights{i,j}.learnFcn to 'learnk'. (Each weight learning parameter property is automatically set to learnk’s default parameters.)

To train the network (or enable it to adapt),

1. Set net.trainParam (or net.adaptParam) properties as desired.

## Algorithms

learnk calculates the weight change dW for a given neuron from the neuron’s input P, output A, and learning rate LR according to the Kohonen learning rule:

dw = lr*(p'-w), if a ~= 0; = 0, otherwise

## References

Kohonen, T., Self-Organizing and Associative Memory, New York, Springer-Verlag, 1984

## Version History

Introduced before R2006a