Asymptotic performance of regularized quadratic discriminant analysis based classifiers
Type
Conference PaperKAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionElectrical Engineering Program
Date
2017-12-13Online Publication Date
2017-12-13Print Publication Date
2017-09Permanent link to this record
http://hdl.handle.net/10754/626960
Metadata
Show full item recordAbstract
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.Citation
Elkhalil K, Kammoun A, Couillet R, Al-Naffouri TY, Alouini M-S (2017) Asymptotic performance of regularized quadratic discriminant analysis based classifiers. 2017 IEEE 27th International Workshop on Machine Learning for Signal Processing (MLSP). Available: http://dx.doi.org/10.1109/MLSP.2017.8168172.Additional Links
http://ieeexplore.ieee.org/document/8168172/ae974a485f413a2113503eed53cd6c53
10.1109/MLSP.2017.8168172