Generative approach to supervised classification of spatio-temporal data via continuous observation hidden Markov model

Abstract

In this article, we develop a novel generative approach to supervised classification of the Spatio-temporal data via parsimoniously parametrized continuous observation Hidden Markov model with label constituting homogeneous Markov chain specified at several fixed spatial locations. The proposed approach is based on the one-step-ahead Bayesian classification of feature observation at each location by using spatial weighting of local Hidden Markov model parameter estimators through neighbouring locations. Parameter estimation procedures are realized by three strategies. They differ in the estimation algorithms for the transition probabilities. The objective of this study is to extend the previous investigations that relied on the particular case of Gaussian Hidden Markov model to continuous observation of Hidden Markov models within general types of emission densities. Motivated by the desire to investigate emission distributions with different support sets, we illustrate our approach to the Hidden Markov models with observations following Gaussian and Beta distributions. Performances of the proposed classifiers are evaluated by the accuracy rate derived from aggregated confusion matrices of one-step Bayesian classification of observations. The numerical analysis of the simulated and real data is carried out. Estimating the parameters of the local Hidden Markov model (Hidden Markov model at a fixed location) is realized by the functions included in the R package “Hidden Markov”. The empirical study is conducted for the critical comparison of the performances of classifiers for particular types of emission densities taking into account three different parameter estimation strategies and various parametric structures. The results of this study can be useful for choosing the most adequate generative supervised classification techniques of the Spatio-temporal data relying on particular types of continuous observation Hidden Markov and various machine learning scenarios.