Learning Hidden Markov Models Using Nonnegative
George V. Cybenko, Valentino Crespi · 2011
The Baum-Welch algorithm together with its deriva- tives 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 associ- ated 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. Index Terms—Hidden Markov models (HMMs), machine learning, nonnegative matrix factorization (NMF).