Performance Evaluations of Gaussian Spatial Data Classifiers Based on Hybrid Actual Error Rate Estimators

Lina Dreiziene,Kestutis Ducinskas

doi:10.17713/ajs.v49i4.1122

Abstract

Discrimination and classification of spatial data has been widely mentioned in the scientific literature, but lacks full mathematical treatment and easily available algorithms and software. This paper fills this gap by introducing the method of statistical classification based on Bayes discriminant function (BDF) and by providing original approach for the classifier performance evaluation. Supervised classification of spatial data with response variable modelled by Gaussian random fields (GRF) with continuous or discrete spatial index is studied. Populations are assumed to be with different regression parameters vectors. Classification rule based on BDF with inserted ML estimators of regression and scale parameters is studied. We focus on the derived actual error rate (AER) and the approximation of the expected error rate (AEER) for both types of models. These are used in the construction of hybrid actual error rate estimators that are spatial modifications of widely applicable D and O estimators applied in cases of independent observations. Simulation experiments are used for comparison of proposed AER estimators by the minimum of unconditional mean squared error criterion for both types of GRF models.

Highlights

Statistical classification and discriminant analysis of spatial data has been mentioned in the scientific literature, but lacks full mathematical treatment and available algorithms and software
In spatial statistics literature conditional autoregressive model (CAR) models are the most often used for the analysis of lattice/areal data since majority of authors declare that CAR models being subclass of Markov random fields are more general than simultaneous regression model (SAR) models
Spatial classification based on plug-in Bayes discriminant function (PBDF) for univariate homogenious CAR (HCAR) models, imposed by the mentioned above structure, is recently explored by Ducinskas and Dreiziene (2018)

Summary

Introduction

Statistical classification and discriminant analysis of spatial data has been mentioned in the scientific literature, but lacks full mathematical treatment and available algorithms and software This paper fills this gap by proposing the method of Gaussian spatial models evaluation and comparison based on classification error rate estimators and by providing novel formulas and algorithms, which allows to evaluate the influence of spatial information to the performance of proposed classifier. Without insignificant loss of generality, we restrict our attention to homogenious CAR (HCAR) lattice models (Song and De Oliveira 2012) with original parametric structure proposed by De Oliveira and Ferreira (2011) These are well-suited to the case of small samples, and ensures good frequentist properties of ML estimators of drift and scale parameters.

Main concepts and definitions

Actual error rates and their estimators

Simulation experiments

Conclusions