Normalized perceptron weight and bias learning function
[dW,LS] = learnpn(W,P,Z,N,A,T,E,gW,gA,D,LP,LS)
info = learnpn('code
')
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 

P 

Z 

N 

A 

T 

E 

gW 

gA 

D 

LP 
Learning parameters, none, 
LS 
Learning state, initially should be = 
and returns
dW 

LS 
New learning state 
info = learnpn('
returns useful
information for each code
')code
string:
'pnames' 
Names of learning parameters 
'pdefaults' 
Default learning parameters 
'needg' 
Returns 1 if this function uses 
Here you define a random input P
and error E
for a
layer with a twoelement 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,[],[],[],[],[])
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 help newp
for adaption and training examples.
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.
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'