Non-negative matrix factorization for parameter estimation in hidden Markov models

Hidden Markov models are well-known in analysis of random processes, which exhibit temporal or spatial structure and have been successfully applied to a wide variety of applications such as but not limited to speech recognition, musical scores, handwriting, and bio-informatics. We present a novel algorithm for estimating the parameters of a hidden Markov model through the application of a non-negative matrix factorization to the joint probability distribution of two consecutive observations. We start with the discrete observation model and extend the results to the continuous observation model through a non-parametric approach of kernel density estimation. For both the cases, we present results on a toy example and compare the performance with the Baum-Welch algorithm.