function [ cluster, cluster_center, cluster_population, cluster_energy, ... it_num ] = hmeans_w_01 ( dim_num, point_num, cluster_num, it_max, point, weight, ... cluster, cluster_center, cluster_population ) %*****************************************************************************80 % %% HMEANS_W_01 applies the weighted H-Means algorithm. % % Discussion: % % The input data for the weight H-Means problem includes: % * a set of N data points X in M dimensions, % * a set of N nonnegative weights W, % * a desired number of clusters K. % * an initial set of cluster centers Z, % * an (optional) initial set of cluster assignments. % % The goal is to determine K points Z, called cluster centers, and % to assign each point X(I) to some cluster Z(J), so that we minimize % the weighted standard deviation of the distance of each data point % to the center of its cluster. Writing J = CLUSTER(I) to % indicate the index of the nearest cluster center Z(J) to the % point X(I), the quantity we are trying to minimize is the sum % of the weighted cluster energies E(J), where: % % E(J) = Sum ( 1 <= I <= N ) W(I) * || X(I) - Z(J) ||**2 % % Here, we assume that we are using the Euclidean norm, so that % % || X(I) - Z(J) ||**2 = Sum ( 1 <= K <= M ) % ( X(I)(K) - Z(J)(K) )**2 % % In this notation, X(I)(K) is the K-th spatial component of the % I-th data point. % % Note that this routine should give the same results as HMEANS_01 % in any case in which all the entries of the WEIGHT vector are equal. % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 04 October 2009 % % Author: % % John Burkardt % % Reference: % % Wendy Martinez, Angel Martinez, % Computational Statistics Handbook with MATLAB, % pages 373-376, % Chapman and Hall / CRC, 2002. % % Parameters: % % Input, integer DIM_NUM, the number of spatial dimensions. % % Input, integer POINT_NUM, the number of data points. % % Input, integer CLUSTER_NUM, the number of clusters. % % Input, integer IT_MAX, the maximum number of iterations. % % Input, real POINT(DIM_NUM,POINT_NUM), the data points. % % Input, real WEIGHT(POINT_NUM), the weights % assigned to the data points. These must be nonnegative, and % at least one must be strictly positive. % % Input, integer CLUSTER(POINT_NUM), the user % may specify an initial cluster for each point, or leave all entries of % CLUSTER set to 0. % % Input, real CLUSTER_CENTER(DIM_NUM,CLUSTER_NUM), the % centers associated with the minimal energy clustering. % % Output, integer CLUSTER(POINT_NUM).the index of the % cluster to which each data point belongs. % % Output, real CLUSTER_CENTER(DIM_NUM,CLUSTER_NUM), the % centers associated with the minimal energy clustering. % % Output, real CLUSTER_ENERGY(CLUSTER_NUM), the energy % associated with each cluster. % % Output, integer IT_NUM, the number of iterations taken. % % % Data checks. % if ( cluster_num < 1 ) fprintf ( 1, '\n' ); fprintf ( 1, 'HMEANS_W_01 - Fatal error!\n' ); fprintf ( 1, ' CLUSTER_NUM < 1.\n' ); error ( 'HMEANS_W_01 - Fatal error!' ) end if ( dim_num < 1 ) fprintf ( 1, '\n' ); fprintf ( 1, 'HMEANS_W_01 - Fatal error!\n' ); fprintf ( 1, ' DIM_NUM < 1.\n' ); error ( 'HMEANS_W_01 - Fatal error!' ) end if ( point_num < 1 ) fprintf ( 1, '\n' ); fprintf ( 1, 'HMEANS_W_01 - Fatal error!\n' ); fprintf ( 1, ' POINT_NUM < 1.\n' ); error ( 'HMEANS_W_01 - Fatal error!' ) end if ( it_max < 0 ) fprintf ( 1, '\n' ); fprintf ( 1, 'HMEANS_W_01 - Fatal error!\n' ); fprintf ( 1, ' IT_MAX < 0.\n' ); error ( 'HMEANS_W_01 - Fatal error!' ) end if ( any ( weight(1:point_num) < 0.0 ) ) fprintf ( 1, '\n' ); fprintf ( 1, 'HMEANS_W_01 - Fatal error!\n' ); fprintf ( 1, ' Some weight entry is negative.\n' ); error ( 'HMEANS_W_01 - Fatal error!' ) end if ( all ( weight(1:point_num) <= 0.0 ) ) fprintf ( 1, '\n' ); fprintf ( 1, 'HMEANS_W_01 - Fatal error!\n' ); fprintf ( 1, ' No weight entry is positive.\n' ); error ( 'HMEANS_W_01 - Fatal error!' ) end % % On input, legal entries in CLUSTER are preserved, but % otherwise, each point is assigned to its nearest cluster. % for i = 1 : point_num if ( cluster(i) <= 0 | cluster_num < cluster(i) ) point_energy_min = Inf; for j = 1 : cluster_num point_energy = sum ( ... ( point(1:dim_num,i) - cluster_center(1:dim_num,j) ).^2 ); if ( point_energy < point_energy_min ) point_energy_min = point_energy; cluster(i) = j; end end end end it_num = 0; while ( it_num < it_max ) it_num = it_num + 1; % % #1: % Reassign points to clusters: % Assign each point to the cluster whose center is nearest; % Count the number of points whose cluster assignment is changed. % swap = 0; for i = 1 : point_num point_energy_min = Inf; c = cluster(i); for j = 1 : cluster_num point_energy = sum ( ... ( point(1:dim_num,i) - cluster_center(1:dim_num,j) ).^2 ); if ( point_energy < point_energy_min ) point_energy_min = point_energy; cluster(i) = j; end end if ( c ~= cluster(i) ) swap = swap + 1; end end % % If no point changed its cluster assignment, the algorithm can make no % more improvements, so terminate. % if ( 1 < it_num ) if ( swap == 0 ) break end end % % Determine the current energy. % energy = 0.0; for i = 1 : point_num energy = energy + weight(i) * sum ( ... ( point(1:dim_num,i) - cluster_center(1:dim_num,cluster(i)) ).^2 ); end % % #2: % Determine the centroids of the clusters, and set the % cluster center to the cluster centroid. % centroid(1:dim_num,1:cluster_num) = 0.0; cluster_population(1:cluster_num) = 0; cluster_weight(1:cluster_num) = 0.0; for i = 1 : point_num c = cluster(i); cluster_population(c) = cluster_population(c) + 1; cluster_weight(c) = cluster_weight(c) + weight(i); centroid(1:dim_num,c) = centroid(1:dim_num,c) ... + weight(i) * point(1:dim_num,i); end missed = 0; for c = 1 : cluster_num if ( cluster_weight(c) ~= 0.0 ) centroid(1:dim_num,c) = centroid(1:dim_num,c) / cluster_weight(c); else missed = missed + 1; centroid(1:dim_num,c) = point(1:dim_num,missed); end end cluster_center(1:dim_num,1:cluster_num) = centroid(1:dim_num,1:cluster_num); end % % Compute the energy based on the final value of the cluster centers. % cluster_energy(1:cluster_num) = 0.0; for i = 1 : point_num c = cluster(i); cluster_energy(c) = cluster_energy(c) + weight(i) * sum ( ... ( point(1:dim_num,i) - cluster_center(1:dim_num,c) ).^2 ); end return end