%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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);

  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  % TODO: 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));
  end

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

end