learnpn

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.

[dW,LS] = learnpn(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` 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

info = learnpn('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.

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,[],[],[],[],[])

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.

Algorithms

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'

Version History

Introduced before R2006a