learnwh (Neural Network Toolbox)

Widrow-Hoff weight/bias learning function

[dW,LS] = learnwh(W,P,Z,N,A,T,E,gW,gA,D,LP,LS)
[db,LS] = learnwh(b,ones(1,Q),Z,N,A,T,E,gW,gA,D,LP,LS)
info = learnwh(code)

Description

learnwh is the Widrow-Hoff weight/bias learning function, and is also known as the delta or least mean squared (LMS) rule.

learnwh(W,P,Z,N,A,T,E,gW,gA,D,LP,LS) takes several inputs,

W - S x R weight matrix (or S x 1 bias vector).

P - R x Q input vectors (or ones(1,Q)).

Z - S x Q weighted input vectors.

N - S x Q net input vectors.

A - S x Q output vectors.

T - S x Q layer target vectors.

E - S x Q layer error vectors.

gW - S x R weight gradient with respect to performance.

gA - S x Q output gradient with respect to performance.

D - S x S neuron distances.

LP - Learning parameters, none, LP = [].

LS - Learning state, initially should be = [].

and returns,

dW - S x R weight (or bias) change matrix.

LS - New learning state.

Learning occurs according to learnwh's learning parameter shown here with its default value.

LP.lr - 0.01 - Learning rate.

learnwh(code) returns useful information for each code string:

'pnames' - Names of learning parameters.

'pdefaults' - Default learning parameters.

'needg' - Returns 1 if this function uses gW or gA.

Examples

Here we define a random input P and error E to a layer with a 2-element input and 3 neurons. We also define the learning rate LR learning parameter.

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

Since learnwh only needs these values to calculate a weight change (see algorithm below), we will use them to do so.

dW = learnwh([],p,[],[],[],[],e,[],[],[],lp,[])

Network Use

You can create a standard network that uses learnwh with newlin.

To prepare the weights and the bias of layer i of a custom network to learn with learnwh:

1.: Set net.trainFcn to 'trainwb'. net.trainParam will automatically become trainwb's default parameters.

2.: Set net.adaptFcn to 'adaptwb'. net.adaptParam will automatically become trainwb's default parameters.

3.: Set each net.inputWeights{i,j}.learnFcn to 'learnwh'. Set each net.layerWeights{i,j}.learnFcn to 'learnwh'. Set net.biases{i}.learnFcn to 'learnwh'.

Each weight and bias learning parameter property will automatically be set to learnwh's default parameters.

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

1.: Set net.trainParam (net.adaptParam) properties to desired values.

2.: Call train(adapt).

See newlin for adaption and training examples.

Algorithm

learnwh calculates the weight change dW for a given neuron from the neuron's input P and error E, and the weight (or bias) learning rate LR, according to the Widrow-Hoff learning rule:

dw = lr*e*pn'