Daniel@0: function [t,r] = db_index(D, cl, C, p, q)
Daniel@0:  
Daniel@0: % DB_INDEX Davies-Bouldin clustering evaluation index.
Daniel@0: %
Daniel@0: % [t,r] = db_index(D, cl, C, p, q)
Daniel@0: %
Daniel@0: %  Input and output arguments ([]'s are optional):  
Daniel@0: %    D     (matrix) data (n x dim)
Daniel@0: %          (struct) map or data struct
Daniel@0: %    cl    (vector) cluster numbers corresponding to data samples (n x 1)
Daniel@0: %    [C]   (matrix) prototype vectors (c x dim) (default = cluster means)
Daniel@0: %    [p]   (scalar) norm used in the computation (default == 2)
Daniel@0: %    [q]   (scalar) moment used to calculate cluster dispersions (default = 2)
Daniel@0: % 
Daniel@0: %    t     (scalar) Davies-Bouldin index for the clustering (=mean(r))
Daniel@0: %    r     (vector) maximum DB index for each cluster (size c x 1)    
Daniel@0: % 
Daniel@0: % See also  KMEANS, KMEANS_CLUSTERS, SOM_GAPINDEX.
Daniel@0: 
Daniel@0: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Daniel@0: %% input arguments
Daniel@0: 
Daniel@0: if isstruct(D), 
Daniel@0:     switch D.type,
Daniel@0:     case 'som_map', D = D.codebook; 
Daniel@0:     case 'som_data', D = D.data; 
Daniel@0:     end
Daniel@0: end
Daniel@0: 
Daniel@0: % cluster centroids
Daniel@0: [l dim] = size(D);
Daniel@0: u = unique(cl); 
Daniel@0: c = length(u); 
Daniel@0: if nargin <3, 
Daniel@0:   C = zeros(c,dim); 
Daniel@0:   for i=1:c, 
Daniel@0:       me = nanstats(D(find(cl==u(i)),:));
Daniel@0:       C(i,:) = me';
Daniel@0:   end 
Daniel@0: end
Daniel@0: 
Daniel@0: u2i = zeros(max(u),1); u2i(u) = 1:c; 
Daniel@0: D = som_fillnans(D,C,u2i(cl)); % replace NaN's with cluster centroid values
Daniel@0: 
Daniel@0: if nargin <4, p = 2; end % euclidian distance between cluster centers
Daniel@0: if nargin <5, q = 2; end % dispersion = standard deviation
Daniel@0:  
Daniel@0: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Daniel@0: %% action
Daniel@0: 
Daniel@0: % dispersion in each cluster 
Daniel@0: for i = 1:c
Daniel@0:   ind = find(cl==u(i)); % points in this cluster
Daniel@0:   l   = length(ind);
Daniel@0:   if l > 0
Daniel@0:     S(i) = (mean(sqrt(sum((D(ind,:) - ones(l,1) * C(i,:)).^2,2)).^q))^(1/q);
Daniel@0:   else
Daniel@0:     S(i) = NaN;
Daniel@0:   end
Daniel@0: end
Daniel@0:  
Daniel@0: % distances between clusters
Daniel@0: %for i = 1:c
Daniel@0: %  for j = i+1:c
Daniel@0: %    M(i,j) = sum(abs(C(i,:) - C(j,:)).^p)^(1/p);
Daniel@0: %  end
Daniel@0: %end
Daniel@0: M = som_mdist(C,p); 
Daniel@0: 
Daniel@0: % Davies-Bouldin index
Daniel@0: R = NaN * zeros(c);
Daniel@0: r = NaN * zeros(c,1);
Daniel@0: for i = 1:c
Daniel@0:   for j = i+1:c
Daniel@0:     R(i,j) = (S(i) + S(j))/M(i,j);
Daniel@0:   end
Daniel@0:   r(i) = max(R(i,:));
Daniel@0: end
Daniel@0:  
Daniel@0: t = mean(r(isfinite(r)));
Daniel@0:  
Daniel@0: return;                                                                                                     
Daniel@0: