A Large Dimensional Analysis of Regularized Discriminant Analysis Classifiers

Handle URI:
http://hdl.handle.net/10754/626453
Title:
A Large Dimensional Analysis of Regularized Discriminant Analysis Classifiers
Authors:
Elkhalil, Khalil ( 0000-0001-7656-3246 ) ; Kammoun, Abla ( 0000-0002-0195-3159 ) ; Couillet, Romain; Al-Naffouri, Tareq Y. ( 0000-0003-2843-5084 ) ; Alouini, Mohamed-Slim ( 0000-0003-4827-1793 )
Abstract:
This article carries out a large dimensional analysis of standard regularized discriminant analysis classifiers designed on the assumption that data arise from a Gaussian mixture model with different means and covariances. 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 mild assumptions, we show that the asymptotic classification error approaches a deterministic quantity that depends only on the means and covariances associated with each class as well as the problem dimensions. Such a result permits a better understanding of the performance of regularized discriminant analsysis, in practical large but finite dimensions, and can be used to determine and pre-estimate the optimal regularization parameter that minimizes the misclassification error probability. Despite being theoretically valid only for Gaussian data, our findings are shown to yield a high accuracy in predicting the performances achieved with real data sets drawn from the popular USPS data base, thereby making an interesting connection between theory and practice.
KAUST Department:
Computer, Electrical, Mathematical Sciences and Engineering, King Abdullah University of Science and Technology
Publisher:
arXiv
Issue Date:
1-Nov-2017
ARXIV:
arXiv:1711.00382
Type:
Preprint
Additional Links:
http://arxiv.org/abs/1711.00382v1; http://arxiv.org/pdf/1711.00382v1
Appears in Collections:
Other/General Submission

Full metadata record

DC FieldValue Language
dc.contributor.authorElkhalil, Khalilen
dc.contributor.authorKammoun, Ablaen
dc.contributor.authorCouillet, Romainen
dc.contributor.authorAl-Naffouri, Tareq Y.en
dc.contributor.authorAlouini, Mohamed-Slimen
dc.date.accessioned2017-12-28T07:32:10Z-
dc.date.available2017-12-28T07:32:10Z-
dc.date.issued2017-11-01en
dc.identifier.urihttp://hdl.handle.net/10754/626453-
dc.description.abstractThis article carries out a large dimensional analysis of standard regularized discriminant analysis classifiers designed on the assumption that data arise from a Gaussian mixture model with different means and covariances. 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 mild assumptions, we show that the asymptotic classification error approaches a deterministic quantity that depends only on the means and covariances associated with each class as well as the problem dimensions. Such a result permits a better understanding of the performance of regularized discriminant analsysis, in practical large but finite dimensions, and can be used to determine and pre-estimate the optimal regularization parameter that minimizes the misclassification error probability. Despite being theoretically valid only for Gaussian data, our findings are shown to yield a high accuracy in predicting the performances achieved with real data sets drawn from the popular USPS data base, thereby making an interesting connection between theory and practice.en
dc.publisherarXiven
dc.relation.urlhttp://arxiv.org/abs/1711.00382v1en
dc.relation.urlhttp://arxiv.org/pdf/1711.00382v1en
dc.rightsArchived with thanks to arXiven
dc.titleA Large Dimensional Analysis of Regularized Discriminant Analysis Classifiersen
dc.typePreprinten
dc.contributor.departmentComputer, Electrical, Mathematical Sciences and Engineering, King Abdullah University of Science and Technologyen
dc.eprint.versionPre-printen
dc.contributor.institutionLaboratoire de Signaux et Systemes (L2S,UMR8506), CNRS-Centrale Supelec-Universite Paris-Suden
dc.identifier.arxividarXiv:1711.00382en
kaust.authorElkhalil, Khalilen
kaust.authorKammoun, Ablaen
kaust.authorAl-Naffouri, Tareq Y.en
kaust.authorAlouini, Mohamed-Slimen
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