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1 function [t,r,Cd,S] = som_gapindex(sM, base, between)
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2
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3 % SOM_GAPINDEX Gap clustering evaluation index.
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4 %
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5 % [t,r] = som_gapindex(sM, base, [between])
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6 %
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7 % Input and output arguments ([]'s are optional):
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8 % sM (struct) map struct
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9 % base (vector) clusters indeces for each map unit, map units
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10 % with index<=0 or NaN are not taken into account
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11 % [between] (vector) indices of prototypes which are "between" clusters:
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12 % the associated distances are doubled
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13 %
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14 % t (scalar) Gap index index for the clustering (=mean(r))
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15 % r (vector) maximum Gap index for each cluster (size max(base) x 1)
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16 %
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17 % See also KMEANS, KMEANS_CLUSTERS, SOM_GAPINDEX.
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18
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19 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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20
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21 if nargin<3, between = find(isnan(base)); end
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22
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23 nc = max(base);
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24 cinds = cell(nc,1);
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25 for i=1:nc, cinds{i} = find(base==i); end
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26
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27 % distances between neighboring prototypes
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28 Ne = som_neighbors(sM,'N1');
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29 Md = som_mdist(sM.codebook,2,[],Ne);
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30 Md(Ne==0) = NaN;
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31
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32 Md(between,:) = Md(between,:)*2;
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33 Md(:,between) = Md(:,between)*2;
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34 Md(between,between) = Md(between,between)/2;
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35
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36 % dispersion in each cluster
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37 S = zeros(nc,1);
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38 for i=1:nc,
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39 inds = setdiff(cinds{i},between);
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40 if any(inds),
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41 indist = Md(inds,inds);
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42 for j=1:size(indist,1), indist(j,j) = NaN; end
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43 indist = indist(isfinite(indist(:)));
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44 if any(indist), S(i) = mean(indist); end
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45 end
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46 end
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47
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48 % distances between clusters
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49 Cd = zeros(nc,nc) + NaN;
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50 for i=1:nc,
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51 inds1 = cinds{i};
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52 for j=1:nc,
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53 inds2 = cinds{j};
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54 od = Md(inds1,inds2);
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55 od = od(isfinite(od(:)));
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56 if any(od), Cd(i,j) = mean(od(:)); end
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57 end
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58 end
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59
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60 % Gap index
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61 R = NaN * zeros(nc);
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62 for i = 1:nc
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63 for j = i+1:nc
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64 R(i,j) = (S(i) + S(j))/Cd(i,j);
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65 R(j,i) = R(i,j);
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66 end
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67 end
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68 r = max(R,[],2);
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69
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70 t = mean(r(isfinite(r)));
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71
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72 return;
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