88 lines
No EOL
3.2 KiB
Matlab
88 lines
No EOL
3.2 KiB
Matlab
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Name: EMG.m
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% Input: x - a nxd matrix (nx3 if using RGB)
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% k - the number of clusters
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% epochs - number of iterations (epochs) to run the algorithm for
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% flag - flag to use improved EM to avoid singular covariance matrix
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% Output: h - a nxk matrix, the expectation of the hidden variable z given the data set and distribution params
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% m - a kxd matrix, the maximum likelihood estimate of the mean
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% Q - vector of values of the complete data log-likelihood function
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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function [h, m, Q] = EMG(x, k, epochs, flag)
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% variables
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num_clusters = k; % number of clusters
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eps = 1e-15; % small value that can be used to avoid obtaining 0's
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lambda = 1e-3; % value for improved version of EM
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[num_data, dim] = size(x);
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h = zeros(num_data, num_clusters); % expectation of data point being part of a cluster
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S = zeros(dim, dim, num_clusters); % covariance matrix for each cluster
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b = zeros(num_data,num_clusters); % cluster assignments, only used for intialization of pi and S
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Q = zeros(epochs*2,1); % vector that can hold complete data log-likelihood after each E and M step
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Initialise cluster means using k-means
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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[~, ~, ~, D] = kmeans(x, k);
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Determine the b values for all data points
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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for i = 1:num_data
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row = D(i,:);
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minIdx = row == min(row);
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b(i,minIdx) = 1;
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end
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Initialize pi's (mixing coefficients)
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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pi = zeros(k, 1);
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for i = 1:k
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pi(i) = sum(b(:, i));
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end
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Initialize the covariance matrix estimate
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% further modifications will need to be made when doing 2(d)
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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m = zeros(k, dim);
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for i = 1:k
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data = x(b(:, i) == 1, :);
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m(i, :) = mean(data);
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S(:, :, i) = cov(data);
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end
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% Main EM loop
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for n=1:epochs
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%%%%%%%%%%%%%%%%
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% E-step
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%%%%%%%%%%%%%%%%
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fprintf('E-step, epoch #%d\n', n);
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[h] = E_step(x, h, pi, m, S, k);
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Store the value of the complete log-likelihood function
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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L = 0;
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for i = 1:num_data
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for j = 1:k
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prior = mvnpdf(x, m(j, :), S(:, :, j));
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L = L + h(i, j) * (log(pi(j)) + log(prior(j)));
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end
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end
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%%%%%%%%%%%%%%%%
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% M-step
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%%%%%%%%%%%%%%%%
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fprintf('M-step, epoch #%d\n', n);
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[Q, S, m] = M_step(x, h, S, k, flag);
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% TODO: Store the value of the complete log-likelihood function
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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end
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end |