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