Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
Pattern recognition: statistical, structural and neural approaches
Pattern recognition: statistical, structural and neural approaches
Linear Discriminant Analysis for Two Classes via Removal of Classification Structure
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Deterministic Annealing Approach for Parsimonious Design of Piecewise Regression Models
IEEE Transactions on Pattern Analysis and Machine Intelligence
Neural Networks: Theoretical Foundations and Analysis
Neural Networks: Theoretical Foundations and Analysis
Pattern Recognition and Neural Networks
Pattern Recognition and Neural Networks
The Foundational Theory of Optimal Bayesian Pairwise Linear Classifiers
Proceedings of the Joint IAPR International Workshops on Advances in Pattern Recognition
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We consider the well-studied Pattern Recognition (PR) problem of designing linear classifiers. When dealing with normally distributed classes, it is well known that the optimal Bayes classifier is linear only when the covariance matrices are equal. This was the only known condition for discriminant linearity. In a previous work, we presented the theoretical framework for optimal pairwise linear classifiers for twodimensional normally distributed random vectors. We derived the necessary and sufficient conditions that the distributions have to satisfy so as to yield the optimal linear classifier as a pair of straight lines.In this paper we extend the previous work to d-dimensional normally distributed random vectors. We provide the necessary and sufficient conditions needed so that the optimal Bayes classifier is a pair of hyperplanes. Various scenarios have been considered including one which resolves the multi-dimensional Mznsky 's paradox for the perceptron. We have also provided some three dimensional examples for all the cases, and tested the classification accuracy of the relevant pairwise linear classifier that we found. In all the cases, these linear classifiers achieve very good performance.