function [ cluster, cluster_center, cluster_population, cluster_energy, ... it_num ] = kmeans_w_01 ( dim_num, point_num, cluster_num, it_max, ... point, weight, cluster_center ) %*****************************************************************************80 % %% KMEANS_W_01 applies the weighted K-Means algorithm. % % Discussion: % % The input data for the weight K-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 KMEANS_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: % % 10 October 2011 % % Author: % % John Burkardt % % Reference: % % David Sparks, % Algorithm AS 58: Euclidean Cluster Analysis, % Applied Statistics, % Volume 22, Number 1, 1973, pages 126-130. % % Parameters: % % Input, integer DIM_NUM, the number of spatial dimensions. % % Input, integer POINT_NUM, the number of 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 points. % % Input, real WEIGHT(POINT_NUM), the weights. % % Input, real CLUSTER_CENTER(DIM_NUM,CLUSTER_NUM), % the cluster centers. % % Output, integer CLUSTER(POINT_NUM), indicates which cluster % each point belongs to. % % Output, real CLUSTER_CENTER(DIM_NUM,CLUSTER_NUM), % the cluster centers. % % Output, integer CLUSTER_POPULATION(CLUSTER_NUM), the number % of points in each cluster. % % Output, real CLUSTER_ENERGY(CLUSTER_NUM), the % cluster energies. % % Output, integer IT_NUM, the number of iterations taken. % it_num = 0; % % Idiot checks. % if ( cluster_num < 1 ) fprintf ( 1, '\n' ); fprintf ( 1, 'KMEANS_W_01 - Fatal error!\n' ); fprintf ( 1, ' CLUSTER_NUM < 1.\n' ); error ( 'KMEANS_W_01 - Fatal error!' ) end if ( dim_num < 1 ) fprintf ( 1, '\n' ); fprintf ( 1, 'KMEANS_W_01 - Fatal error!\n' ); fprintf ( 1, ' DIM_NUM < 1.\n' ); error ( 'KMEANS_W_01 - Fatal error!' ) end if ( point_num < 1 ) fprintf ( 1, '\n' ); fprintf ( 1, 'KMEANS_W_01 - Fatal error!\n' ); fprintf ( 1, ' POINT_NUM < 1.\n' ); error ( 'KMEANS_W_01 - Fatal error!' ) end if ( it_max < 0 ) fprintf ( 1, '\n' ); fprintf ( 1, 'KMEANS_W_01 - Fatal error!\n' ); fprintf ( 1, ' IT_MAX < 0.\n' ); error ( 'KMEANS_W_01 - Fatal error!' ) end if ( any ( weight(1:point_num) < 0.0 ) ) fprintf ( 1, '\n' ); fprintf ( 1, 'KMEANS_W_01 - Fatal error!\n' ); fprintf ( 1, ' Some weight entry is negative.\n' ); error ( 'KMEANS_W_01 - Fatal error!' ) end if ( all ( weight(1:point_num) <= 0.0 ) ) fprintf ( 1, '\n' ); fprintf ( 1, 'KMEANS_W_01 - Fatal error!\n' ); fprintf ( 1, ' No weight entry is positive.\n' ); error ( 'KMEANS_W_01 - Fatal error!' ) end % % Assign each point to the nearest cluster. % for i = 1 : point_num for j = 1 : cluster_num cluster_energy(j) = sum ( ... ( point(1:dim_num,i) - cluster_center(1:dim_num,j) ).^2 ); end [ dummy, cluster(i) ] = min ( cluster_energy(1:cluster_num) ); end % % Determine the cluster populations and weights. % cluster_population(1:cluster_num) = 0; cluster_weight(1:cluster_num) = 0.0; for i = 1 : point_num j = cluster(i); cluster_population(j) = cluster_population(j) + 1; cluster_weight(j) = cluster_weight(j) + weight(i); end % % Calculate the mean and sum of squares for each cluster. % cluster_center(1:dim_num,1:cluster_num) = 0.0; for i = 1 : point_num j = cluster(i); cluster_center(1:dim_num,j) = cluster_center(1:dim_num,j) ... + weight(i) * point(1:dim_num,i); end for i = 1 : cluster_num if ( 0.0 < cluster_weight(i) ) cluster_center(1:dim_num,i) = cluster_center(1:dim_num,i) ... / cluster_weight(i); end end % % Set the point energies. % f(1:point_num) = 0.0; for i = 1 : point_num j = cluster(i); f(i) = sum ( ( point(1:dim_num,i) - cluster_center(1:dim_num,j) ).^2 ); end % % Set the cluster energies. % cluster_energy(1:cluster_num) = 0.0; for i = 1 : point_num j = cluster(i); cluster_energy(j) = cluster_energy(j) + weight(i) * f(i); end % % Adjust the point energies by a weight factor. % for i = 1 : point_num j = cluster(i); if ( weight(i) < cluster_weight(j) ) f(i) = f(i) * cluster_weight(j) / ( cluster_weight(j) - weight(i) ); end end % % Examine each observation in turn to see if it should be % reassigned to a different cluster. % it_num = 0; while ( it_num < it_max ) it_num = it_num + 1; swap = 0; for i = 1 : point_num il = cluster(i); ir = il; if ( cluster_population(il) <= 1 ) continue end dc = f(i); for j = 1 : cluster_num if ( j ~= il ) de = sum ( ... ( point(1:dim_num,i) - cluster_center(1:dim_num,j) ).^2 ) ... * cluster_weight(j) / ( cluster_weight(j) + weight(i) ); if ( de < dc ) dc = de; ir = j; end end end % % If the lowest value was obtained by staying in the current cluster, % then cycle. % if ( ir == il ) continue end % % Reassign the point from cluster IL to cluster IR. % cluster_center(1:dim_num,il) = ... ( cluster_weight(il) * cluster_center(1:dim_num,il) ... - weight(i) * point(1:dim_num,i) ) ... / ( cluster_weight(il) - weight(i) ); cluster_center(1:dim_num,ir) = ... ( cluster_weight(ir) * cluster_center(1:dim_num,ir) ... + weight(i) * point(1:dim_num,i) ) ... / ( cluster_weight(ir) + weight(i) ); cluster_weight(il) = cluster_weight(il) - weight(i); cluster_weight(ir) = cluster_weight(ir) + weight(i); cluster_energy(il) = cluster_energy(il) - f(i); cluster_energy(ir) = cluster_energy(ir) + dc; cluster_population(ir) = cluster_population(ir) + 1; cluster_population(il) = cluster_population(il) - 1; cluster(i) = ir; % % Adjust the value of F for all points in clusters IL and IR. % for j = 1 : point_num k = cluster(j); if ( k == il | k == ir ) f(j) = sum ( ... ( point(1:dim_num,j) - cluster_center(1:dim_num,k) ).^2 ); if ( weight(j) < cluster_weight(k) ) f(j) = f(j) * cluster_weight(k) ... / ( cluster_weight(k) - weight(j) ); end end end swap = swap + 1; end % % Exit if no reassignments were made during this iteration. % if ( swap == 0 ) break end 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