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Linear vs. quadratic discriminant analysis classifier: a tutorial

Linear vs. quadratic discriminant analysis classifier: a tutorial The aim of this paper is to collect in one place the basic background needed to understand the discriminant analysis (DA) classifier to make the reader of all levels be able to get a better understanding of the DA and to know how to apply this classifier in different applications. This paper starts with basic mathematical definitions of the DA steps with visual explanations of these steps. Moreover, in a step-by-step approach, a number of numerical examples were illustrated to show how to calculate the discriminant functions and decision boundaries when the covariance matrices of all classes were common or not. The singularity problem of DA was explained and some of the state-of-the-art solutions to this problem were highlighted with numerical illustrations. An experiment is conducted to compare between the linear and quadratic classifiers and to show how to solve the singularity problem when high-dimensional datasets are used. Keywords: linear discriminant classifier; LDC; quadratic discriminant classifier QDC; classification; singularity problem; discriminant function; decision boundaries; subspace method; regularised linear discriminant analysis; RLDA. Reference to this paper should be made as follows: Tharwat, A. (2016) `Linear vs. quadratic discriminant analysis classifier: a tutorial', Int. J. Applied Pattern Recognition, Vol. 3, http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Applied Pattern Recognition Inderscience Publishers

Linear vs. quadratic discriminant analysis classifier: a tutorial

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References (27)

Publisher
Inderscience Publishers
Copyright
Copyright © 2016 Inderscience Enterprises Ltd.
ISSN
2049-887X
eISSN
2049-8888
DOI
10.1504/IJAPR.2016.079050
Publisher site
See Article on Publisher Site

Abstract

The aim of this paper is to collect in one place the basic background needed to understand the discriminant analysis (DA) classifier to make the reader of all levels be able to get a better understanding of the DA and to know how to apply this classifier in different applications. This paper starts with basic mathematical definitions of the DA steps with visual explanations of these steps. Moreover, in a step-by-step approach, a number of numerical examples were illustrated to show how to calculate the discriminant functions and decision boundaries when the covariance matrices of all classes were common or not. The singularity problem of DA was explained and some of the state-of-the-art solutions to this problem were highlighted with numerical illustrations. An experiment is conducted to compare between the linear and quadratic classifiers and to show how to solve the singularity problem when high-dimensional datasets are used. Keywords: linear discriminant classifier; LDC; quadratic discriminant classifier QDC; classification; singularity problem; discriminant function; decision boundaries; subspace method; regularised linear discriminant analysis; RLDA. Reference to this paper should be made as follows: Tharwat, A. (2016) `Linear vs. quadratic discriminant analysis classifier: a tutorial', Int. J. Applied Pattern Recognition, Vol. 3,

Journal

International Journal of Applied Pattern RecognitionInderscience Publishers

Published: Jan 1, 2016

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