Neural Network Toolbox

learnlv2

LVQ2.1 weight learning function

Syntax

[dW,LS] = learnlv2(W,P,Z,N,A,T,E,gW,gA,D,LP,LS)

info = learnlv2(code)

Description

learnlv2 is the LVQ2 weight learning function.

learnlv2(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 learnlv1's learning parameter, shown here with its default value.

• LP.lr - 0.01 -- Learning rate

  LP.window - 0.25 -- Window size (0 to 1, typically 0.2 to 0.3)

learnlv2(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 sample input P, output A, weight matrix W, and output gradient gA for a layer with a two-element input and three neurons.

We also define the learning rate LR.

• p = rand(2,1);
  w = rand(3,2);
  n = negdist(w,p);
  a = compet(n);
  gA = [-1;1; 1];
  lp.lr = 0.5;
  

Since learnlv2 only needs these values to calculate a weight change (see algorithm below), we will use them to do so.

• dW = learnlv2(w,p,[],n,a,[],[],[],gA,[],lp,[])
  

Network Use

You can create a standard network that uses learnlv2 with newlvq.

To prepare the weights of layer i of a custom network to learn with learnlv2

1. Set net.trainFcn to 'trainr'. (net.trainParam will automatically become trainr's default parameters.)
2. Set net.adaptFcn to 'trains'. (net.adaptParam will automatically become trains's default parameters.)
3. Set each net.inputWeights{i,j}.learnFcn to 'learnlv2'. Set each net.layerWeights{i,j}.learnFcn to 'learnlv2'. (Each weight learning parameter property will automatically be set to learnlv2's default parameters.)

To train the network (or enable it to adapt)

1. Set net.trainParam (or net.adaptParam) properties as desired.
2. Call train (or adapt).

Algorithm

learnlv2 implements Learning Vector Quantization 2.1, which works as follows:

For each presentation, if the winning neuron i should not have won, and the runner up j should have, and the distance di between the winning neuron and the input p is roughly equal to the distance dj from the runner up neuron to the input p according to the given window,

• min(di/dj, dj/di) > (1-window)/(1+window)
  

then move the winning neuron i weights away from the input vector, and move the runner up neuron j weights toward the input according to:

• dw(i,:) = - lp.lr*(p'-w(i,:))
  dw(j,:) = + lp.lr*(p'-w(j,:))
  

See Also

learnlv1, adapt, train

learnlv1

learnos

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