function [Neurons] = neural_gas(D,n,epochs,alpha0,lambda0)
%NEURAL_GAS Quantizes the data space using the neural gas algorithm.
%
% Neurons = neural_gas(D, n, epochs, [alpha0], [lambda0])
%
% C = neural_gas(D,50,10);
% sM = som_map_struct(sD);
% sM.codebook = neural_gas(sD,size(sM.codebook,1),10);
%
% Input and output arguments ([]'s are optional):
% D (matrix) the data matrix, size dlen x dim
% (struct) a data struct
% n (scalar) the number of neurons
% epochs (scalar) the number of training epochs (the number of
% training steps is dlen*epochs)
% [alpha0] (scalar) initial step size, 0.5 by default
% [lambda0] (scalar) initial decay constant, n/2 by default
%
% Neurons (matrix) the neuron matrix, size n x dim
%
% See also SOM_MAKE, KMEANS.
% References:
% T.M.Martinetz, S.G.Berkovich, and K.J.Schulten. "Neural-gas" network
% for vector quantization and its application to time-series prediction.
% IEEE Transactions on Neural Networks, 4(4):558-569, 1993.
% Contributed to SOM Toolbox vs2, February 2nd, 2000 by Juha Vesanto
% Copyright (c) by Juha Vesanto
% http://www.cis.hut.fi/projects/somtoolbox/
% juuso 101297 020200
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Check arguments and initialize
error(nargchk(3, 5, nargin)); % check the number of input arguments
if isstruct(D), D = D.data; end
[dlen,dim] = size(D);
Neurons = (rand(n,dim)-0.5)*10e-5; % small initial values
train_len = epochs*dlen;
if nargin<4 | isempty(alpha0) | isnan(alpha0), alpha0 = 0.5; end
if nargin<5 | isempty(lambda0) | isnan(lambda0), lambda0 = n/2; end
% random sample order
rand('state',sum(100*clock));
sample_inds = ceil(dlen*rand(train_len,1));
% lambda
lambda = lambda0 * (0.01/lambda0).^([0:(train_len-1)]/train_len);
% alpha
alpha = alpha0 * (0.005/alpha0).^([0:(train_len-1)]/train_len);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Action
for i=1:train_len,
% sample vector
x = D(sample_inds(i),:); % sample vector
known = ~isnan(x); % its known components
X = x(ones(n,1),known); % we'll need this
% neighborhood ranking
Dx = Neurons(:,known) - X; % difference between vector and all map units
[qerrs, inds] = sort((Dx.^2)*known'); % 1-BMU, 2-BMU, etc.
ranking(inds) = [0:(n-1)];
h = exp(-ranking/lambda(i));
H = h(ones(length(known),1),:)';
% update
Neurons = Neurons + alpha(i)*H.*(x(ones(n,1),known) - Neurons(:,known));
% track
fprintf(1,'%d / %d \r',i,train_len);
if 0 & mod(i,50) == 0,
hold off, plot3(D(:,1),D(:,2),D(:,3),'bo')
hold on, plot3(Neurons(:,1),Neurons(:,2),Neurons(:,3),'r+')
drawnow
end
end
fprintf(1,'\n');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%