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The use of quadratic discriminant analysis (QDA) or its regularized version(R-QDA) for classification is often not recommended, due to itswell-acknowledged high sensitivity to the estimation noise of the covariancematrix. This becomes all the more the case in unbalanced data settings forwhich it has been found that R-QDA becomes equivalent to the classifier thatassigns all observations to the same class. In this paper, we propose animproved R-QDA that is based on the use of two regularization parameters and amodified bias, properly chosen to avoid inappropriate behaviors of R-QDA inunbalanced settings and to ensure the best possible classification performance.The design of the proposed classifier builds on a refined asymptotic analysisof its performance when the number of samples and that of features grow largesimultaneously, which allows to cope efficiently with the high-dimensionalityfrequently met within the big data paradigm. The performance of the proposedclassifier is assessed on both real and synthetic data sets and was shown to bemuch better than what one would expect from a traditional R-QDA.

Improved Design of Quadratic Discriminant Analysis Classifier in Unbalanced Settings