Learning Hidden Markov Models Using Nonnegative Matrix Factorization

The Baum-Welch algorithm together with its derivatives and variations has been the main technique for learning hidden Markov models (HMMs) from observational data. We present an HMM learning algorithm based on the nonnegative matrix factorization (NMF) of higher order Markovian statistics that is structurally different from the Baum-Welch and its associated approaches. The described algorithm supports estimation of the number of recurrent states of an HMM and iterates the NMF algorithm to improve the learned HMM parameters. Numerical examples are provided as well.