Correct Classification Rates in Multi-Category Discriminant Analysis of Spatial Gaussian Data

Lina Dreižienė^1,2, Kęstutis Dučinskas¹, Laura Paulionienė¹

¹Department of Mathematics and Statistics, Klaipeda University, Klaipeda, Lithuania.
²Institute of Mathematics and Informatics, Vilnius University, Vilnius, Lithuania.

DOI: 10.4236/ojs.2015.51003                

Abstract

This paper discusses the problem of classifying a multivariate Gaussian random field observation into one of the several categories specified by different parametric mean models. Investigation is conducted on the classifier based on plug-in Bayes classification rule (PBCR) formed by replacing unknown parameters in Bayes classification rule (BCR) with category parameters estimators. This is the extension of the previous one from the two category cases to the multi-category case. The novel closed-form expressions for the Bayes classification probability and actual correct classification rate associated with PBCR are derived. These correct classification rates are suggested as performance measures for the classifications procedure. An empirical study has been carried out to analyze the dependence of derived classification rates on category parameters.

Keywords

Gaussian Random Field, Bayes Classification Rule, Pairwise Discriminant Function, Actual Correct Classification Rate

Conflicts of Interest

The authors declare no conflicts of interest.

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