learnpn :: Functions (Neural Network Toolbox™)

learnpn

Purpose

Normalized perceptron weight and bias learning function

Syntax

[dW,LS] = learnpn(W,P,Z,N,A,T,E,gW,gA,D,LP,LS)
info = learnpn(code)

Description

learnpn is a weight and bias learning function. It can result in faster learning than learnp when input vectors have widely varying magnitudes.

learnpn(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 = []

`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

`dW`	`S` x `R` weight (or bias) change matrix
`LS`	New learning state

learnpn(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

`'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.

```
p = rand(2,1);
e = rand(3,1);
```

Because learnpn only needs these values to calculate a weight change (see algorithm below), use them to do so.

dW = learnpn([],p,[],[],[],[],e,[],[],[],[],[])

Network Use

You can create a standard network that uses learnpn with newp.

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

Set net.trainFcn to 'trainb'. (net.trainParam automatically becomes trainb's default parameters.)
Set net.adaptFcn to 'trains'. (net.adaptParam automatically becomes trains's default parameters.)
Set each net.inputWeights{i,j}.learnFcn to 'learnpn'. Set each net.layerWeights{i,j}.learnFcn to 'learnpn'. Set net.biases{i}.learnFcn to 'learnpn'. (Each weight and bias learning parameter property automatically becomes the empty matrix, because learnpn has no learning parameters.)

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

Set net.trainParam (or net.adaptParam) properties to desired values.
Call train (adapt).

See newp for adaption and training examples.

Algorithm

learnpn calculates the weight change dW for a given neuron from the neuron's input P and error E according to the normalized perceptron learning rule:

pn = p / sqrt(1 + p(1)^2 + p(2)^2) + ... + p(R)^2)
dw = 0,  if e = 0
     = pn', if e = 1
     = -pn', if e = -1

The expression for dW can be summarized as

```
dw = e*pn'
```

Limitations

Perceptrons do have one real limitation. The set of input vectors must be linearly separable if a solution is to be found. That is, if the input vectors with targets of 1 cannot be separated by a line or hyperplane from the input vectors associated with values of 0, the perceptron will never be able to classify them correctly.