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1 function [t,r] = db_index(D, cl, C, p, q)
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2
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3 % DB_INDEX Davies-Bouldin clustering evaluation index.
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4 %
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5 % [t,r] = db_index(D, cl, C, p, q)
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6 %
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7 % Input and output arguments ([]'s are optional):
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8 % D (matrix) data (n x dim)
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9 % (struct) map or data struct
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10 % cl (vector) cluster numbers corresponding to data samples (n x 1)
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11 % [C] (matrix) prototype vectors (c x dim) (default = cluster means)
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12 % [p] (scalar) norm used in the computation (default == 2)
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13 % [q] (scalar) moment used to calculate cluster dispersions (default = 2)
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14 %
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15 % t (scalar) Davies-Bouldin index for the clustering (=mean(r))
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16 % r (vector) maximum DB index for each cluster (size c x 1)
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17 %
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18 % See also KMEANS, KMEANS_CLUSTERS, SOM_GAPINDEX.
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19
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20 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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21 %% input arguments
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22
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23 if isstruct(D),
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24 switch D.type,
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25 case 'som_map', D = D.codebook;
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26 case 'som_data', D = D.data;
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27 end
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28 end
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29
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30 % cluster centroids
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31 [l dim] = size(D);
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32 u = unique(cl);
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33 c = length(u);
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34 if nargin <3,
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35 C = zeros(c,dim);
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36 for i=1:c,
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37 me = nanstats(D(find(cl==u(i)),:));
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38 C(i,:) = me';
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39 end
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40 end
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41
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42 u2i = zeros(max(u),1); u2i(u) = 1:c;
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43 D = som_fillnans(D,C,u2i(cl)); % replace NaN's with cluster centroid values
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44
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45 if nargin <4, p = 2; end % euclidian distance between cluster centers
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46 if nargin <5, q = 2; end % dispersion = standard deviation
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47
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48 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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49 %% action
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50
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51 % dispersion in each cluster
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52 for i = 1:c
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53 ind = find(cl==u(i)); % points in this cluster
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54 l = length(ind);
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55 if l > 0
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56 S(i) = (mean(sqrt(sum((D(ind,:) - ones(l,1) * C(i,:)).^2,2)).^q))^(1/q);
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57 else
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58 S(i) = NaN;
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59 end
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60 end
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61
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62 % distances between clusters
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63 %for i = 1:c
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64 % for j = i+1:c
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65 % M(i,j) = sum(abs(C(i,:) - C(j,:)).^p)^(1/p);
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66 % end
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67 %end
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68 M = som_mdist(C,p);
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69
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70 % Davies-Bouldin index
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71 R = NaN * zeros(c);
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72 r = NaN * zeros(c,1);
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73 for i = 1:c
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74 for j = i+1:c
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75 R(i,j) = (S(i) + S(j))/M(i,j);
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76 end
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77 r(i) = max(R(i,:));
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78 end
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79
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80 t = mean(r(isfinite(r)));
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81
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82 return;
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83
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