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Communication Dans Un Congrès Année : 2017

Asymptotic performance of regularized quadratic discriminant analysis based classifiers

Khalil Elkhalil
  • Fonction : Auteur
Romain Couillet
Tareq Al-Naffouri
  • Fonction : Auteur

Résumé

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.
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Dates et versions

hal-01957741 , version 1 (19-05-2020)

Identifiants

Citer

Khalil Elkhalil, Abla Kammoun, Romain Couillet, Tareq Al-Naffouri, Mohamed-Slim Alouini. Asymptotic performance of regularized quadratic discriminant analysis based classifiers. 2017 IEEE 27th International Workshop on Machine Learning for Signal Processing (MLSP), 2017, Tokyo, Japan. ⟨10.1109/mlsp.2017.8168172⟩. ⟨hal-01957741⟩
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