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1 function [P,V,me,l] = pcaproj(D,arg1,arg2)
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2
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3 %PCAPROJ Projects data vectors using Principal Component Analysis.
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4 %
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5 % [P,V,me,l] = pcaproj(D, odim)
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6 % P = pcaproj(D, V, me)
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7 %
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8 % Input and output arguments ([]'s are optional)
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9 % D (matrix) size dlen x dim, the data matrix
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10 % (struct) data or map struct
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11 % odim (scalar) how many principal vectors are used
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12 %
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13 % P (matrix) size dlen x odim, the projections
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14 % V (matrix) size dim x odim, principal eigenvectors (unit length)
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15 % me (vector) size 1 x dim, center point of D
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16 % l (vector) size 1 x odim, the corresponding eigenvalues,
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17 % relative to total sum of eigenvalues
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18 %
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19 % See also SAMMON, CCA.
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20
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21 % Contributed to SOM Toolbox 2.0, February 2nd, 2000 by Juha Vesanto
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22 % Copyright (c) by Juha Vesanto
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23 % http://www.cis.hut.fi/projects/somtoolbox/
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24
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25 % juuso 191297 070200
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26
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27 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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28
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29 error(nargchk(2, 3, nargin)); % check the number of input arguments
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30
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31 % the data
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32 if isstruct(D),
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33 if strcmp(D.type,'som_map'), D=D.codebook; else D=D.data; end
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34 end
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35 [dlen dim] = size(D);
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36
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37 if nargin==2,
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38
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39 odim = arg1;
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40
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41 % autocorrelation matrix
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42 A = zeros(dim);
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43 me = zeros(1,dim);
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44 for i=1:dim,
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45 me(i) = mean(D(isfinite(D(:,i)),i));
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46 D(:,i) = D(:,i) - me(i);
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47 end
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48 for i=1:dim,
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49 for j=i:dim,
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50 c = D(:,i).*D(:,j); c = c(isfinite(c));
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51 A(i,j) = sum(c)/length(c); A(j,i) = A(i,j);
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52 end
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53 end
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54
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55 % eigenvectors, sort them according to eigenvalues, and normalize
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56 [V,S] = eig(A);
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57 eigval = diag(S);
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58 [y,ind] = sort(abs(eigval));
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59 eigval = eigval(flipud(ind));
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60 V = V(:,flipud(ind));
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61 for i=1:odim, V(:,i) = (V(:,i) / norm(V(:,i))); end
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62
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63 % take only odim first eigenvectors
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64 V = V(:,1:odim);
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65 l = abs(eigval)/sum(abs(eigval));
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66 l = l(1:odim);
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67
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68 else % nargin==3,
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69
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70 V = arg1;
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71 me = arg2;
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72 odim = size(V,2);
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73 D = D-me(ones(dlen,1),:);
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74
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75 end
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76
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77 % project the data using odim first eigenvectors
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78 P = D*V;
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79
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80 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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