Quadratic Discriminant Analysis of Spatially Correlated Data
Articles
K. Dučinskas
Klaipėda University, Lithuania
J. Šaltytė
Klaipėda University, Lithuania
Published 2001-12-05
https://doi.org/10.15388/NA.2001.6.1.15212
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Keywords

Bayesian classification rule
quadratic discriminant function
training samples, expected error rate
asymptotic expansion

How to Cite

Dučinskas, K. and Šaltytė, J. (2001) “Quadratic Discriminant Analysis of Spatially Correlated Data”, Nonlinear Analysis: Modelling and Control, 6(2), pp. 15–28. doi:10.15388/NA.2001.6.1.15212.

Abstract

The problem of classification of the realisation of the stationary univariate Gaussian random field into one of two populations with different means and different factorised covariance matrices is considered. In such a case optimal classification rule in the sense of minimum probability of misclassification is associated with non-linear (quadratic) discriminant function. Unknown means and the covariance matrices of the feature vector components are estimated from spatially correlated training samples using the maximum likelihood approach and assuming spatial correlations to be known. Explicit formula of Bayes error rate and the first-order asymptotic expansion of the expected error rate associated with quadratic plug-in discriminant function are presented. A set of numerical calculations for the spherical spatial correlation function is performed and two different spatial sampling designs are compared.

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