csci5521/assignments/hwk03/M_step.m
2023-11-18 02:40:46 -06:00

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2.5 KiB
Matlab

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Name: M_step.m
% Input: x - a nxd matrix (nx3 if using RGB)
% Q - vector of values from the complete data log-likelihood function
% h - a nxk matrix, the expectation of the hidden variable z given the data set and distribution params
% S - cluster covariance matrices
% k - the number of clusters
% flag - flag to use improved EM to avoid singular covariance matrix
% Output: S - cluster covariance matrices
% m - cluster means
% pi - mixing coefficients
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [S, m, pi] = M_step(x, h, S, k, flag)
% get size of data
[num_data, dim] = size(x);
eps = 1e-15;
lambda = 1e-3; % value for improved version of EM
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% update mixing coefficients
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
N_i = zeros(k, 1);
m = zeros(k, dim);
for i = 1:k
N_i(i) = sum(h(:, i));
for j = 1:num_data
m(i, :) = m(i, :) + h(j, i) * x(j, :);
end
end
pi = N_i / num_data;
for i = 1:k
m(i, :) = m(i, :) ./ N_i(i);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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
s = zeros(dim, dim) + eye(dim) * eps;
for j = 1:num_data
s = s + h(j, i) * (x(j, :) - m(i, :))' * (x(j, :) - m(i, :));
end
s = s / N_i(i);
% 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;
% https://www.mathworks.com/matlabcentral/answers/57411-matlab-sometimes-produce-a-covariance-matrix-error-with-non-postive-semidefinite#answer_69524
% [V, D] = eig(s);
% s = V * max(D, eps) / V;
S(:, :, i) = s;
end
if flag
for i = 1:k
S(:, :, i) = S(:, :, i) + lambda * eye(dim) / 2;
end
end
end