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% 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
%        S - cluster covariance matrices
%        k - the number of clusters
% Output: Q - vector of values of the complete data log-likelihood function
%         S - cluster covariance matrices
%         m - cluster means
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function [Q, S, m] = M_step(x, Q, h, S, k)
     
    % get size of data
    [num_data, dim] = size(x);
    eps = 1e-15;
    lambda = 1e-3; % value for improved version of EM 

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    % TODO: update mixing coefficients
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    % TODO: update cluster means
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    % TODO: Calculate the covariance matrix estimate 
    %       further modifications will need to be made when doing 2(d)
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    
end