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1 function [Neurons] = neural_gas(D,n,epochs,alpha0,lambda0)
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2
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3 %NEURAL_GAS Quantizes the data space using the neural gas algorithm.
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4 %
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5 % Neurons = neural_gas(D, n, epochs, [alpha0], [lambda0])
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6 %
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7 % C = neural_gas(D,50,10);
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8 % sM = som_map_struct(sD);
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9 % sM.codebook = neural_gas(sD,size(sM.codebook,1),10);
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10 %
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11 % Input and output arguments ([]'s are optional):
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12 % D (matrix) the data matrix, size dlen x dim
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13 % (struct) a data struct
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14 % n (scalar) the number of neurons
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15 % epochs (scalar) the number of training epochs (the number of
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16 % training steps is dlen*epochs)
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17 % [alpha0] (scalar) initial step size, 0.5 by default
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18 % [lambda0] (scalar) initial decay constant, n/2 by default
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19 %
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20 % Neurons (matrix) the neuron matrix, size n x dim
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21 %
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22 % See also SOM_MAKE, KMEANS.
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23
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24 % References:
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25 % T.M.Martinetz, S.G.Berkovich, and K.J.Schulten. "Neural-gas" network
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26 % for vector quantization and its application to time-series prediction.
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27 % IEEE Transactions on Neural Networks, 4(4):558-569, 1993.
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28
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29 % Contributed to SOM Toolbox vs2, February 2nd, 2000 by Juha Vesanto
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30 % Copyright (c) by Juha Vesanto
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31 % http://www.cis.hut.fi/projects/somtoolbox/
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32
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33 % juuso 101297 020200
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34
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35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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36 %% Check arguments and initialize
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37
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38 error(nargchk(3, 5, nargin)); % check the number of input arguments
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39
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40 if isstruct(D), D = D.data; end
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41 [dlen,dim] = size(D);
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42 Neurons = (rand(n,dim)-0.5)*10e-5; % small initial values
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43 train_len = epochs*dlen;
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44
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45 if nargin<4 | isempty(alpha0) | isnan(alpha0), alpha0 = 0.5; end
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46 if nargin<5 | isempty(lambda0) | isnan(lambda0), lambda0 = n/2; end
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47
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48 % random sample order
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49 rand('state',sum(100*clock));
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50 sample_inds = ceil(dlen*rand(train_len,1));
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51
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52 % lambda
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53 lambda = lambda0 * (0.01/lambda0).^([0:(train_len-1)]/train_len);
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54
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55 % alpha
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56 alpha = alpha0 * (0.005/alpha0).^([0:(train_len-1)]/train_len);
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57
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58 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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59 %% Action
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60
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61 for i=1:train_len,
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62
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63 % sample vector
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64 x = D(sample_inds(i),:); % sample vector
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65 known = ~isnan(x); % its known components
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66 X = x(ones(n,1),known); % we'll need this
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67
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68 % neighborhood ranking
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69 Dx = Neurons(:,known) - X; % difference between vector and all map units
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70 [qerrs, inds] = sort((Dx.^2)*known'); % 1-BMU, 2-BMU, etc.
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71 ranking(inds) = [0:(n-1)];
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72 h = exp(-ranking/lambda(i));
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73 H = h(ones(length(known),1),:)';
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74
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75 % update
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76 Neurons = Neurons + alpha(i)*H.*(x(ones(n,1),known) - Neurons(:,known));
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77
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78 % track
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79 fprintf(1,'%d / %d \r',i,train_len);
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80 if 0 & mod(i,50) == 0,
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81 hold off, plot3(D(:,1),D(:,2),D(:,3),'bo')
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82 hold on, plot3(Neurons(:,1),Neurons(:,2),Neurons(:,3),'r+')
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83 drawnow
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84 end
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85 end
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86
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87 fprintf(1,'\n');
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88
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89 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
