gaussian_mixture_template.py

 
def gaussian_mixture(data, K, init_method, epsilon, niterations, plotflag, RSEED=123):
    '''
    % Template for a function to fit  a Gaussian mixture model via EM 
    % using K mixture components. The data are contained in the N x d "data" matrix. 
    %  
    % INPUTS
    %  data: N x d real-valued data matrix
    %  K: number of clusters (mixture components)
    %  initialization_method: 1 for memberships, 2 for parameters, 3 for kmeans 
    %  epsilon: convergence threshold used to detect convergence
    %  niterations (optional): maximum number of iterations to perform (default 500)
    %  plotflag (optional): equals 1 to plot parameters during learning, 
    %                       0 for no plotting (default is 0)
    %  RSEED (optional): initial seed value for the random number generator
    %  
    %
    % OUTPUTS
    %  gparams: K-dim structure array containing the learned mixture model parameters: 
    %           gparams(k).weight = weight of component k
    %           gparams(k).mean = d-dimensional mean vector for kth component 
    %           gparams(k).covariance = d x d covariance vector for kth component
    %  memberships: N x K matrix of probability memberships for "data"
    %
    %  Note: Interpretation of gparams and memberships:
    %
    %    - gparams(k).weight is the probability that a randomly selected row
    %         belongs to component (or cluster) i (so it is "cluster size")
    %
    %    - memberships(i,k) = p(cluster k | x) which is the probability
    %         (computed via Bayes rule) that vector x was generated by cluster
    %         k, according to the "generative" probabilistic model. 
    '''

    # your code goes here....

    # initialize....

    # perform E-step...

    # perform M-step...

    # compute log-likelihood and print to screen.....

    # check for convergence.....

    return gparams, memberships