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