learnwh

Widrow-Hoff weight/bias learning function

Syntax

```[dW,LS] = learnwh(W,P,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.

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

 `W` `S`-by-`R` weight matrix (or `b`, and `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` weight 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 the `learnwh` learning parameter, shown here with its default value.

 `LP.lr — 0.01` Learning rate

`info = learnwh('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` and error `E` for a layer with a two-element input and three neurons. You also define the learning rate `LR` learning parameter.

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

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

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

Network Use

You can create a standard network that uses `learnwh` with `linearlayer`.

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

1. Set `net.trainFcn` to `'trainb'`. `net.trainParam` automatically becomes `trainb`’s default parameters.

2. Set `net.adaptFcn` to `'trains'`. `net.adaptParam` automatically becomes `trains`’s default parameters.

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

4. Set each `net.layerWeights{i,j}.learnFcn` to `'learnwh'`.

5. Set `net.biases{i}.learnFcn` to `'learnwh'`. Each weight and bias learning parameter property is automatically set to the `learnwh` default parameters.

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

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

2. Call `train` (or `adapt`).

Algorithms

`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' ```

References

Widrow, B., and M.E. Hoff, “Adaptive switching circuits,” 1960 IRE WESCON Convention Record, New York IRE, pp. 96–104, 1960

Widrow, B., and S.D. Sterns, Adaptive Signal Processing, New York, Prentice-Hall, 1985

Version History

Introduced before R2006a