%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Name: E_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
%        pi - vector of mixing coefficients
%        m - cluster means
%        S - cluster covariance matrices
%        k - the number of clusters
% Output: h - a nxk matrix, the expectation of the hidden variable z given the data set and distribution params
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [h] = E_step(x, h, pi, m, S, k)

  [num_data, ~] = size(x);

  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  % perform E-step of EM algorithm
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  parts = zeros(num_data, k);

  for i = 1:k
    parts(:, i) = pi(i) * mvnpdf(x, m(i, :), S(:, :, i));
  end

  s = sum(parts);
  for j = 1:num_data
    h(j, :) = parts(j, :) ./ s;
  end

end