dcl.m

FISMAT accommodates different arithmetic operators, fuzzification and defuzzification algorithm, imp

function [y2,m2x,m2y]=dcl(samples,p,c,wii,wij,rands)

% [y2,m2x,m2y]= dcl(samples,p,c,wii,wij,rands)
%
% Stochastic Unsupervised-Differential-Competive-Learning (DCL) algorithm.
%
% An autoassociative AVQ  two-layer feedforward neural network is trained by
% the sample vectors in 'samples' with competive learning. The input field
% neuronal field Fx receives the sample data and passes it forward through 
% synaptic connection matrix M to the p competing neurons in field Fy. The
% metaphor of competing neurons reduces to nearest neighbor classification.
% The system compares the current vector random sample x(t) in Euclidian 
% distance to the p synaptic vectors m1(t),...,mp(t). If the jth synaptic
% vector is closest to x(t), then the jth neuron "wins" the competition for
% activation at time t. The jth competing neuron should behave as a class
% indicator function: Sj=IDj. More generally the jth Fy neuron only esti-
% mates IDj. 
% rands is a vector of random permutations: 
% rands=randperm(number_of_samples)
%
% Reference:
% Kong, Kosko : 'Differential Competive Learning for Centroid Estimation
% and Phoneme Recognition'. 
% IEEE Transcactions on Neural Networks, Vol.2, No.1, Jan.1991
% pp.118-124
%
% FSTB - Fuzzy Systems Toolbox for MATLAB
% Copyright (c) 1993-1996 by Olaf Wolkenhauer
% Control Systems Centre at UMIST
% Manchester M60 1QD, UK
%
% 20-May-1994

% p=  number of synaptic vectors mj defining p columns of the synaptic
%     connection matrix M.
%     p is also equal to the number of competing nonlinear neurons in the
%     output field, Fy.
% n=  number of inputs or linear neurons in the input neuronal field, Fx.
% M=  synaptic connection matrix, which interconnects the input field with 
%     the output field.
% x=  matrix which stores all training sample vectors. One vector in a row.
%     In this function the variable is called 'samples'.
% W=  pxp matrix containing the Fy within-field synaptic connection 
%     strengths. Diagonal elements wii are positive, off-diagonal elements
%     negative. 
% yt= Fy neuronal activations. yt equals y(t) and yt1 equals y(t+1).

% Competive AVQ Algorithm
%
% The AVQ system compares a current vector random sample x(t) in Euclidean
% distance to the p columns of the matrix M.

% 1.) Initialize synaptic vectors: mi(0)=x(i) , i=1,...,p. 
% 2.) For random sample x(t), find the closest or "winning" synaptic vector
%     mj(t). (nearest neighbor classification)
%     Define N synaptic vectors closest to x as "winners".
% 3.) Update the winning synaptic vector(s) mj(t) with an appropriate learn-
%     ing algorithm.


[nu_of_v,n]=size(samples); % nu_of_v equals the number of sample vectors.
% Observing yt(1) and M(1,2):
y2=zeros(1,nu_of_v);
m2x=zeros(1,nu_of_v);
m2y=zeros(1,nu_of_v);
M=zeros(n,p);
%wii=1;  Positive diagonal elements - winning neurons excites themselves 
%wij=-1; and inhibit all other neurons. => Off-diagonal elements negative.
W=wij.*ones(p,p)+(wii+abs(wij)).*eye(p,p); % other pos. or neg.values ? ? ?
yt=zeros(1,p);                  % initialisation ? ? ?
yt1=yt;

% Initialisation: 
% (sample dependence avoids pathologies disturbing the nearest neigbor 
%  learning)
for i=1:p,
  M(:,i)=samples(i,:)'; 
end;
% If x is randomly chosed, no on-line calculation possible ? ? ? 
% rands=randperm(nu_of_v); 
eunorm=ones(1,p);        % For measuring the distance to a sample vector.

runtime=clock;
for t=1:nu_of_v,
  % For random sample x(t) find the closest synaptic vector mj(t):
  sample=samples(rands(t),:);
  for i=1:p,
    eunorm(i)=norm(M(:,i)-sample');
  end;
  [winnorm, j]=min(eunorm);
  % Updating the Fy neuronal activations yi with an additive model:
  % Nonnegative signal function approximating a steep binary logistic 
  % sigmoid, with some constant c>0 :
  % c=1;                                   
  Syt=1./(1+exp(-c.*yt));              
  yt1=yt+(sample*M)+Syt*W;
  y2(t)=yt1(2);
  % Updating the winning synaptic vector(s) mj(t) with the differential
  % competive learning algorithm:
  % ct=1/t;
  % harmonic series coefficient for a decreasing gain sequence over
  % the learning period. For fast robust stochastic approximation, 
  % only the h.s.c satisfy the contraints in [Kong].
  ct=0.1*(1-(t/nu_of_v));
  % Activation difference as an approximation of the competive signal 
  % difference DSj:
  Dyjt=sign(yt1(j)-yt(j));
  M(:,j)=M(:,j)+ct*Dyjt.*(sample'-M(:,j));
  yt=yt1; 
  plot(M(1,:),M(2,:),'.','EraseMode','none'); drawnow
  m2x(t)=M(1,2);
  m2y(t)=M(2,2);
end; % of outer t loop for the DCL training period.
runtime=etime(clock,runtime)