Performance of the supervised generative classifiers of spatio-temporal areal data using various spatial autocorrelation indexes

This article is concerned with a generative approach to supervised classification of spatio-temporal data collected at fixed areal units and modeled by Gaussian Markov random field. We focused on the classifiers based on Bayes discriminant functions formed by the log-ratio of the class conditional likelihoods. As a novel modeling contribution, we propose to use decision threshold values induced by three popular spatial autocorrelation indexes, i.e., Moran's I, Geary's C and Getis-Ord G. The goal of this study is to extend the recent investigations in the context of geostatistical and hidden Markov Gaussian models to one in the context of areal Gaussian Markov models. The classifiers performance measures are chosen to be the average accuracy rate, which shows the percentage of correctly classified test data, balanced accuracy rate specified by the average of sensitivity and specificity and the geometric mean of sensitivity and specificity. The proposed methodology is illustrated using 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. Classification model selection procedure is illustrated on three data sets with class labels specified by the threshold to mortality index due to acute cardiovascular event, malignant neoplasms and diseases of the circulatory system. Presented critical comparison among proposed approach classifiers with various spatial autocorrelation indexes (decision threshold values) and classifier based hidden Markov model can aid in the selection of proper classification techniques for the spatio-temporal areal data.