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ok kinda works?

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This commit is contained in:
Michael Zhang 2023-11-16 02:46:02 -06:00
parent b444304a89
commit bc30320eef
3 changed files with 44 additions and 30 deletions
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26
assignments/hwk03/EMG.m
View file

@ -22,12 +22,12 @@ function [h, m, Q] = EMG(x, k, epochs, flag)
Q = zeros(epochs*2,1); % vector that can hold complete data log-likelihood after each E and M step
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Initialise cluster means using k-means
% TODO: Initialise cluster means using k-means
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[~, ~, ~, D] = kmeans(x, k);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Determine the b values for all data points
% TODO: Determine the b values for all data points
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i = 1:num_data
row = D(i,:);
@ -36,7 +36,7 @@ function [h, m, Q] = EMG(x, k, epochs, flag)
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Initialize pi's (mixing coefficients)
% TODO: Initialize pi's (mixing coefficients)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
pi = zeros(k, 1);
for i = 1:k
@ -44,8 +44,8 @@ function [h, m, Q] = EMG(x, k, epochs, flag)
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Initialize the covariance matrix estimate
% further modifications will need to be made when doing 2(d)
% TODO: Initialize the covariance matrix estimate
% further modifications will need to be made when doing 2(d)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
m = zeros(k, dim);
for i = 1:k
@ -63,21 +63,21 @@ function [h, m, Q] = EMG(x, k, epochs, flag)
[h] = E_step(x, h, pi, m, S, k);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Store the value of the complete log-likelihood function
% TODO: Store the value of the complete log-likelihood function
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
L = 0;
for i = 1:num_data
for j = 1:k
prior = mvnpdf(x, m(j, :), S(:, :, j));
L = L + h(i, j) * (log(pi(j)) + log(prior(j)));
end
end
% for i = 1:num_data
% for j = 1:k
% prior = mvnpdf(x, m(j, :), S(:, :, j));
% L = L + h(i, j) * (log(pi(i)) + log(prior(i)));
% end
% end
%%%%%%%%%%%%%%%%
% M-step
%%%%%%%%%%%%%%%%
fprintf('M-step, epoch #%d\n', n);
[Q, S, m] = M_step(x, h, S, k, flag);
[S, m, pi] = M_step(x, h, S, k, flag);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% TODO: Store the value of the complete log-likelihood function

10
assignments/hwk03/E_step.m
View file

@ -14,17 +14,17 @@ function [h] = E_step(x, h, pi, m, S, k)
[num_data, ~] = size(x);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% TODO: perform E-step of EM algorithm
% perform E-step of EM algorithm
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
parts = zeros(num_data, k);
for j = 1:k
parts(:, j) = pi(j) * mvnpdf(x, m(j, :), S(:, :, j));
for i = 1:k
parts(:, i) = pi(i) * mvnpdf(x, m(i, :), S(:, :, i));
end
s = sum(parts);
for i = 1:num_data
h(i, :) = parts(i, :) ./ s;
for j = 1:num_data
h(j, :) = parts(j, :) ./ s;
end
end

36
assignments/hwk03/M_step.m
View file

@ -21,24 +21,38 @@ function [S, m, pi] = M_step(x, h, S, k, flag)
% update mixing coefficients
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
pi = zeros(k, 1);
for i = 1:num_data
row = h(i, :);
maxValue = max(row);
maxIdx = find(row == maxValue);
pi(maxIdx) = pi(maxIdx) + 1;
N_i = zeros(k, 1);
for i = 1:k
N_i(i) = sum(h(:, i));
end
pi = pi ./ num_data;
pi = N_i / num_data;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% TODO: update cluster means
% update cluster means
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
m = zeros(k, dim);
m = h' * x ./ N_i;
% for i = 1:k
% m(i, :) = sum(h(:, i) .* x(i, :)) / N_i(i);
% end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% TODO: Calculate the covariance matrix estimate
% further modifications will need to be made when doing 2(d)
% Calculate the covariance matrix estimate
% further modifications will need to be made when doing 2(d)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
S = zeros(dim, dim, k);
for i = 1:k
% for j = 1:num_data
% S(:, :, i) = S(:, :, i) + h(j, i) * (x(j, :) - m(i, :)) * (x(j, :) - m(i, :))';
% end
s = (x - m(i, :))' * ((x - m(i, :)) .* h(:, i)) / N_i(i);
% % MAKE IT SYMMETRIC https://stackoverflow.com/a/38730499
% S(:, :, i) = (s + s') / 2;
% https://www.mathworks.com/matlabcentral/answers/366140-eig-gives-a-negative-eigenvalue-for-a-positive-semi-definite-matrix#answer_290270
s = (s + s') / 2;
[V, D] = eig(s);
S(:, :, i) = V * max(D,eps) / V;
end
end