EM for HMM Multivariate Gaussian processes

A fast implementation of the EM Algorithm for HMM Multivariate Gaussian Mixture

em_ghmm : Expectation-Maximization algorithm for a HMM with Multivariate Gaussian measurement

Usage

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[logl , PI , A , M , S] = em_ghmm(Z , PI0 , A0 , M0 , S0 , [options]);

Inputs

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Z Measurements (m x K x n1 x ... x nl)

PI0 Initial probabilities (d x 1) : Pr(x_1 = i) , i=1,...,d. PI0 can be (d x 1 x v1 x ... x vr)

A0 Initial state transition probabilities matrix Pr(x_{k} = i| x_{k - 1} = j) such

sum_{x_k}(A0) = 1 => sum(A , 1) = 1. A0 can be (d x d x v1 x ... x vr).

M0 Initial mean vector. M0 can be (m x 1 x d x v1 x ... x vr)

S0 Initial covariance matrix. S0 can be (m x m x d x v1 x ... x vr)

options nb_ite Number of iteration (default [30])

update_PI Update PI (0/1 = no/[yes])

update_A Update PI (0/1 = no/[yes])

update_M Update M (0/1 = no/[yes])

update_S Update S (0/1 = no/[yes])

Outputs

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logl Final loglikelihood (n1 x ... x nl x v1 x ... x vr)

PI Estimated initial probabilities (d x 1 x n1 x ... x nl v1 x ... x vr)

A Estimated state transition probabilities matrix (d x d x n1 x ... x nl v1 x ... x vr)

M Estimated mean vector (m x 1 x d x n1 x ... x nl v1 x ... x vr)

S Estimated covariance vector (m x m x d x n1 x ... x nl v1 x ... x vr)

Please run mexme_em_ghmm to compile mex files on your platform.

Run test_em_ghmm for demo