ok kinda works?
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3 changed files with 44 additions and 30 deletions
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@ -22,12 +22,12 @@ function [h, m, Q] = EMG(x, k, epochs, flag)
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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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% TODO: 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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% TODO: 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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@ -36,7 +36,7 @@ function [h, m, Q] = EMG(x, k, epochs, flag)
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end
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Initialize pi's (mixing coefficients)
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% TODO: 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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@ -44,8 +44,8 @@ function [h, m, Q] = EMG(x, k, epochs, flag)
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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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% TODO: 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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@ -63,21 +63,21 @@ function [h, m, Q] = EMG(x, k, epochs, flag)
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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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% TODO: 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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% 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(i)) + log(prior(i)));
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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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[S, m, pi] = 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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@ -14,17 +14,17 @@ function [h] = E_step(x, h, pi, m, S, k)
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[num_data, ~] = size(x);
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% TODO: perform E-step of EM algorithm
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% perform E-step of EM algorithm
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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parts = zeros(num_data, k);
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for j = 1:k
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parts(:, j) = pi(j) * mvnpdf(x, m(j, :), S(:, :, j));
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for i = 1:k
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parts(:, i) = pi(i) * mvnpdf(x, m(i, :), S(:, :, i));
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end
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s = sum(parts);
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for i = 1:num_data
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h(i, :) = parts(i, :) ./ s;
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for j = 1:num_data
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h(j, :) = parts(j, :) ./ s;
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end
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end
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@ -21,24 +21,38 @@ function [S, m, pi] = M_step(x, h, S, k, flag)
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% update mixing coefficients
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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pi = zeros(k, 1);
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for i = 1:num_data
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row = h(i, :);
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maxValue = max(row);
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maxIdx = find(row == maxValue);
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pi(maxIdx) = pi(maxIdx) + 1;
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N_i = zeros(k, 1);
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for i = 1:k
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N_i(i) = sum(h(:, i));
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end
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pi = pi ./ num_data;
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pi = N_i / num_data;
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% TODO: update cluster means
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% update cluster means
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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m = zeros(k, dim);
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m = h' * x ./ N_i;
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% for i = 1:k
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% m(i, :) = sum(h(:, i) .* x(i, :)) / N_i(i);
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% end
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% TODO: Calculate the covariance matrix estimate
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% further modifications will need to be made when doing 2(d)
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% Calculate 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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S = zeros(dim, dim, k);
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for i = 1:k
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% for j = 1:num_data
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% S(:, :, i) = S(:, :, i) + h(j, i) * (x(j, :) - m(i, :)) * (x(j, :) - m(i, :))';
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% end
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s = (x - m(i, :))' * ((x - m(i, :)) .* h(:, i)) / N_i(i);
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% % MAKE IT SYMMETRIC https://stackoverflow.com/a/38730499
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% S(:, :, i) = (s + s') / 2;
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% https://www.mathworks.com/matlabcentral/answers/366140-eig-gives-a-negative-eigenvalue-for-a-positive-semi-definite-matrix#answer_290270
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s = (s + s') / 2;
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[V, D] = eig(s);
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S(:, :, i) = V * max(D,eps) / V;
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end
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end
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