[Master Index] [Index for export/lyngby]

lyngby_km_bic

(export/lyngby/lyngby_km_bic.m)


Function Synopsis

bic = lyngby_km_bic(X, Centers, Assign, varargin)

Help text

 lyngby_km_bic        - Bayesian information criterion for K-means

       bic = lyngby_km_bic(X, Assign, Centers, varargin)

       Input:  X        Data matrix
               Center   Cluster centers
               Assign   Assignment vector

       Output  bic      BIC 

       Bayesian information criterion (BIC) for K-means that is
       computed as the log likelihood penalized with a term
      
          BIC = log[ P(X|C, sigma2) ] - (K*P+1)/2 * log(N)

       where X is the data matrix, C the centers, sigma2 the variance
       (which here is estimated), (K*P+1) is the number of
       paramenters in the model (K clusters on a P-dimensional
       problem) and N is the number of objects in the X(N x P) data
       matrix. 

       Example: 
         load iris.txt
         for n = 1:50
           [C,A] = lyngby_km_main(iris, 'type', 'mean', 'clusters', n, 'init', 'random');
           l(n) = lyngby_km_loglikelihood(iris, C, A, 'sigmatype', 'unbiased');
           bic(n) = lyngby_km_bic(iris, C, A);
         end
         plot([l ; bic]'), xlabel('Clusters')
         ylabel('Log likelihood/bic');

       See also LYNGBY, LYNGBY_KM_MAIN, LYNGBY_KM_LOGLIKELIHOOD,
                LYNGBY_KM_WITHIN.

 $Id: lyngby_km_bic.m,v 1.2 2005/09/27 21:57:13 fnielsen Exp $

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