Asymptotic performance of regularized quadratic discriminant analysis based classifiers

Khalil Elkhalil, Abla Kammoun, Romain Couillet, Tareq Y. Al-Naffouri, Mohamed-Slim Alouini

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

Abstract

This paper carries out a large dimensional analysis of the standard regularized quadratic discriminant analysis (QDA) classifier designed on the assumption that data arise from a Gaussian mixture model. The analysis relies on fundamental results from random matrix theory (RMT) when both the number of features and the cardinality of the training data within each class grow large at the same pace. Under some mild assumptions, we show that the asymptotic classification error converges to a deterministic quantity that depends only on the covariances and means associated with each class as well as the problem dimensions. Such a result permits a better understanding of the performance of regularized QDA and can be used to determine the optimal regularization parameter that minimizes the misclassification error probability. Despite being valid only for Gaussian data, our theoretical findings are shown to yield a high accuracy in predicting the performances achieved with real data sets drawn from popular real data bases, thereby making an interesting connection between theory and practice.
Original languageEnglish (US)
Title of host publication2017 IEEE 27th International Workshop on Machine Learning for Signal Processing (MLSP)
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Pages1-6
Number of pages6
ISBN (Print)9781509063413
DOIs
StatePublished - Dec 13 2017

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01

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