function [t,r,Cd,S] = som_gapindex(sM, base, between) % SOM_GAPINDEX Gap clustering evaluation index. % % [t,r] = som_gapindex(sM, base, [between]) % % Input and output arguments ([]'s are optional): % sM (struct) map struct % base (vector) clusters indeces for each map unit, map units % with index<=0 or NaN are not taken into account % [between] (vector) indices of prototypes which are "between" clusters: % the associated distances are doubled % % t (scalar) Gap index index for the clustering (=mean(r)) % r (vector) maximum Gap index for each cluster (size max(base) x 1) % % See also KMEANS, KMEANS_CLUSTERS, SOM_GAPINDEX. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% if nargin<3, between = find(isnan(base)); end nc = max(base); cinds = cell(nc,1); for i=1:nc, cinds{i} = find(base==i); end % distances between neighboring prototypes Ne = som_neighbors(sM,'N1'); Md = som_mdist(sM.codebook,2,[],Ne); Md(Ne==0) = NaN; Md(between,:) = Md(between,:)*2; Md(:,between) = Md(:,between)*2; Md(between,between) = Md(between,between)/2; % dispersion in each cluster S = zeros(nc,1); for i=1:nc, inds = setdiff(cinds{i},between); if any(inds), indist = Md(inds,inds); for j=1:size(indist,1), indist(j,j) = NaN; end indist = indist(isfinite(indist(:))); if any(indist), S(i) = mean(indist); end end end % distances between clusters Cd = zeros(nc,nc) + NaN; for i=1:nc, inds1 = cinds{i}; for j=1:nc, inds2 = cinds{j}; od = Md(inds1,inds2); od = od(isfinite(od(:))); if any(od), Cd(i,j) = mean(od(:)); end end end % Gap index R = NaN * zeros(nc); for i = 1:nc for j = i+1:nc R(i,j) = (S(i) + S(j))/Cd(i,j); R(j,i) = R(i,j); end end r = max(R,[],2); t = mean(r(isfinite(r))); return;

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