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 initializeerror(nargchk(3, 5, nargin));  % check the number of input argumentsif isstruct(D), D = D.data; end[dlen,dim] = size(D);Neurons = (rand(n,dim)-0.5)*10e-5; % small initial valuestrain_len = epochs*dlen;if nargin<4 | isempty(alpha0) | isnan(alpha0), alpha0 = 0.5; endif nargin<5 | isempty(lambda0) | isnan(lambda0), lambda0 = n/2; end% random sample orderrand('state',sum(100*clock));sample_inds = ceil(dlen*rand(train_len,1));% lambdalambda = lambda0 * (0.01/lambda0).^([0:(train_len-1)]/train_len);% alphaalpha = alpha0 * (0.005/alpha0).^([0:(train_len-1)]/train_len);%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Actionfor 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  endendfprintf(1,'\n');%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%