function [pd,Pdm,pmd] = som_probability_gmm(D, sM, K, P) %SOM_PROBABILITY_GMM Probabilities based on a gaussian mixture model. % % [pd,Pdm,pmd] = som_probability_gmm(D, sM, K, P) % % [K,P] = som_estimate_gmm(sM,D); % [pd,Pdm,pmd] = som_probability_gmm(D,sM,K,P); % som_show(sM,'color',pmd(:,1),'color',Pdm(:,1)) % % Input and output arguments: % D (matrix) size dlen x dim, the data for which the % (struct) data struct, probabilities are calculated % sM (struct) map struct % (matrix) size munits x dim, the kernel centers % K (matrix) size munits x dim, kernel width parameters % computed by SOM_ESTIMATE_GMM % P (matrix) size 1 x munits, a priori probabilities for each % kernel computed by SOM_ESTIMATE_GMM % % pd (vector) size dlen x 1, probability of each data vector in % terms of the whole gaussian mixture model % Pdm (matrix) size munits x dlen, probability of each vector in % terms of each kernel % pmd (matrix) size munits x dlen, probability of each vector to % have been generated by each kernel % % See also SOM_ESTIMATE_GMM. % Contributed to SOM Toolbox vs2, February 2nd, 2000 by Esa Alhoniemi % Copyright (c) by Esa Alhoniemi % http://www.cis.hut.fi/projects/somtoolbox/ % ecco 180298 juuso 050100 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % input arguments if isstruct(sM), M = sM.codebook; else M = sM; end [c dim] = size(M); if isstruct(D), D = D.data; end dlen = size(D,1); % reserve space for output variables pd = zeros(dlen,1); if nargout>=2, Pdm = zeros(c,dlen); end if nargout==3, pmd = zeros(c,dlen); end % the parameters of each kernel cCoeff = cell(c,1); cCoinv = cell(c,1); for m=1:c, co = diag(K(m,:)); cCoinv{m} = inv(co); cCoeff{m} = 1 / ((2*pi)^(dim/2)*det(co)^.5); end % go through the vectors one by one for i=1:dlen, x = D(i,:); % compute p(x|m) pxm = zeros(c,1); for m = 1:c, dx = M(m,:) - x; pxm(m) = cCoeff{m} * exp(-.5 * dx * cCoinv{m} * dx'); %pxm(m) = normal(dx, zeros(1,dim), diag(K(m,:))); end pxm(isnan(pxm(:))) = 0; % p(x|m) if nargin>=2, Pdm(:,i) = pxm; end % P(x) = P(x|M) = sum( P(m) * p(x|m) ) pd(i) = P*pxm; % p(m|x) = p(x|m) * P(m) / P(x) if nargout==3, pmd(:,i) = (P' .* pxm) / pd(i); end end return; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % subfunction normal % % computes probability of x when mean and covariance matrix % of a distribution are known function result = normal(x, mu, co) [l dim] = size(x); coinv = inv(co); coeff = 1 / ((2*pi)^(dim/2)*det(co)^.5); diff = x - mu; result = coeff * exp(-.5 * diff * coinv * diff');

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