function [init_state_prob, transmat, mixmat, mu, Sigma] =  init_mhmm(data, Q, M, cov_type, left_right)% INIT_MHMM Compute initial param. estimates for an HMM with mixture of Gaussian outputs.% [init_state_prob, transmat, obsmat, mixmat, mu, Sigma] = init_mhmm(data, Q, M, cov_type, left_right)%% Inputs:% data(:,t,l) = observation vector at time t in sequence l% Q = num. hidden states% M = num. mixture components% cov_type = 'full', 'diag' or 'spherical'% left_right = 1 if the model is a left-to-right HMM, 0 otherwise%% Outputs:% init_state_prob(i) = Pr(Q(1) = i)% transmat(i,j) = Pr(Q(t+1)=j | Q(t)=i)% mixmat(j,k) = Pr(M(t)=k | Q(t)=j) where M(t) is the mixture component at time t% mu(:,j,k) = mean of Y(t) given Q(t)=j, M(t)=k% Sigma(:,:,j,k) = cov. of Y(t) given Q(t)=j, M(t)=kO = size(data, 1);T = size(data, 2);nex = size(data, 3);data = reshape(data, [O T*nex]);init_state_prob = normalise(ones(Q,1));transmat = mk_stochastic(ones(Q,Q));if M > 1  mixmat = mk_stochastic(rand(Q,M));else  mixmat = ones(Q, 1);endif 0  Sigma = repmat(eye(O), [1 1 Q M]);  % Initialize each mean to a random data point  indices = randperm(T);  mu = reshape(data(:,indices(1:(Q*M))), [O Q M]);end% Initialize using K-means, where K = Q*M% We should really segment the sequence uniformly into Q strips,% and run M-means on each segment.mix = gmm(O, Q*M, cov_type);options = foptions;max_iter = 5;options(14) = max_iter;mix = gmminit(mix, data', options);mu = reshape(mix.centres', [O Q M]);i = 1;for q=1:Q  for m=1:M    switch cov_type      case 'diag',	Sigma(:,:,q,m) = diag(mix.covars(i,:));      case 'full',	Sigma(:,:,q,m) = mix.covars(:,:,i);      case 'spherical',	Sigma(:,:,q,m) = mix.covars(i) * eye(O);    end    i = i + 1;  endend