Abstract
Paper deals with statistical classification of spatial data as a part of widely applicable statistical approach to pattern recognition. Error rates in supervised classification of Gaussian random field observation into one of two populations specified by different constant means and common stationary geometric anisotropic covariance are considered. Formula for the exact Bayesian error rate is derived. The influence of the ratio of anisotropy to the error rates is evaluated numerically for the case of complete parametric certainty.
Highlights
The extension of classical statistical classification techniques in spatial data analysis is a problem of practical interest
Switzer [5]) was the first to treat classification of spatial data, a work that was expended by Mardia [3]
Geometric anisotropy means that models of the covariances have the same nugget, sill but different ranges in to perpendicular directions (Wackernagel, [6])
Summary
The extension of classical statistical classification techniques in spatial data analysis is a problem of practical interest. In this paper we derived formula for Bayes error rate assuming that training sample observations and an observation to be classified are spatially correlated. 1. Statistical models for spatial population In this paper, we consider the performances of BCR and plug-in BCR with parameters estimators from training sample. Geometric anisotropy means that models of the covariances (or semivariograms) have the same nugget, sill but different ranges in to perpendicular directions (Wackernagel, [6]). If one plots the directional ranges in 2D case they would fall on the edge of an ellipse, where major and minor axes of ellipse correspond to the largest and shortest ranges of directional semivariograms It adds to the isotropic model two more parameters: the anisotropy angle j and anisotropy ratio λ = Rangemax > 1. Procedures of fitting of the geometrically anisotropic semivariogram models to the environmental data can be realised by software system R package Gstat (see [2])
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
