A novel approach for modeling positive vectors with inverted Dirichlet-based hidden Markov models

Abstract

Hidden Markov Models (HMMs) are among the most remarkably powerful probabilistic models, that although been acknowledged for decades have recently made a huge resurgence in the machine learning field. Their ever-growing use to model diversified and heterogeneous data (image,video, audio, time series) in numerous important practical situations is the subject of all forms of perpetual extensions. This work presents what we believe to be the first integration of the Inverted Dirichlet (ID) Mixture Models into the framework of HMMs. The proposed method uses the inverted Dirichlet mixtures to model the emission probabilities also known as observation probabilities. This extension (IDHMM), is motivated by the proven capacity of these mixtures to deal with positive vectors and overcome mixture models’ capability to take into account any ordering or temporal constraints relative to information. The complete inference and parameter estimation are detailed in this work. Applications in the context of image categorization and indoor occupancy detection demonstrate higher performance compared to the extensively used Gaussian mixture-based Hidden Markov Model (GHMM) and the Dirichlet mixture-based hidden Markov Model (DHMM).