Simultaneous positive sequential vectors modeling and unsupervised feature selection via continuous hidden Markov models

Abstract Since positive data vectors are often naturally generated in various real-life applications, positive vectors modeling has become an important research topic. In this article, we tackle the problem of modeling positive sequential vectors through continuous hidden Markov models (HMMs). Motivated by several recent studies in which the generalized inverted Dirichlet (GID) distribution has provided better performance than the Gaussian distribution for modeling positive data, instead of adopting Gaussian mixture models (GMM) as the emission density for conventional continuous HMMs, we theoretically propose a novel HMM by considering the mixture of GID distributions as the emission density. Moreover, to cope with high-dimensional data which may contain irrelevant features, an unsupervised localized feature selection method is incorporated with our model, which results in a unified framework that can simultaneously perform positive sequential data modeling and feature selection. To learn the proposed model, we develop a convergence-guaranteed algorithm based on variational Bayes. The advantages of our model are demonstrated through both simulated data sets and a real-life application about human action recognition.