Spatially Weighted Bayesian Classification of Spatio-Temporal Areal Data Based on Gaussian-Hidden Markov Models

This article is concerned with an original approach to generative classification of spatiotemporal areal (or lattice) data based on implementation of spatial weighting to Hidden Markov Models (HMMs). In the framework of this approach data model at each areal unit is specified by conditionally independent Gaussian observations and first-order Markov chain for labels and call it local HMM. The proposed classification is based on modification of conventional HMM by the implementation of spatially weighted estimators of local HMMs parameters. We focus on classification rules based on Bayes discriminant function (BDF) with plugged in the spatially weighted parameter estimators obtained from the labeled training sample. For each local HMM, the estimators of regression coefficients and variances and two types of transition probabilities are used in two levels (higher and lower) of spatial weighting. The average accuracy rate (ACC) and balanced accuracy rate (BAC), computed from confusion matrices evaluated from a test sample, are used as performance measures of classifiers. The proposed methodology is illustrated for simulated data and for real dataset, i.e., annual death rate data collected by the Institute of Hygiene of the Republic of Lithuania from the 60 municipalities in the period from 2001 to 2019. Critical comparison of proposed classifiers is done. The experimental results showed that classifiers based on HMM with higher level of spatial weighting in majority cases have advantage in spatial-temporal consistency and classification accuracy over one with lower level of spatial weighting.