## On Optimal Pairwise Linear Classifiers for Normal Distributions: The Two-Dimensional Case (2001)

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### BibTeX

@MISC{Rueda01onoptimal,

author = {Luis Rueda and B. John Oommen},

title = {On Optimal Pairwise Linear Classifiers for Normal Distributions: The Two-Dimensional Case},

year = {2001}

}

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### Abstract

Computing linear classifiers is a very important problem in statistical Pattern Recognition (PR). These classifiers have been investigated by the PR community extensively since they are the ones which are both easy to implement and comprehend. It is well known that when dealing with normally distributed classes, the optimal discriminant function for two-classes is linear only when the covariance matrices are equal. Other approaches, such as the Fisher's discriminant, the perceptron algorithm, minimum square distance classifiers, etc., have solved this problem by generating a linear classifier in normal and non-normal distributions, but these classifiers are typically suboptimal. In this