  Quadratic discriminant analysis (QDA) is a widely used classification
technique that generalizes the linear discriminant analysis (LDA) classifier to
the case of distinct covariance matrices among classes. For the QDA classifier
to yield high classification performance, an accurate estimation of the
covariance matrices is required. Such a task becomes all the more challenging
in high dimensional settings, wherein the number of observations is comparable
with the feature dimension. A popular way to enhance the performance of QDA
classifier under these circumstances is to regularize the covariance matrix,
giving the name regularized QDA (R-QDA) to the corresponding classifier. In
this work, we consider the case in which the population covariance matrix has a
spiked covariance structure, a model that is often assumed in several
applications. Building on the classical QDA, we propose a novel quadratic
classification technique, the parameters of which are chosen such that the
fisher-discriminant ratio is maximized. Numerical simulations show that the
proposed classifier not only outperforms the classical R-QDA for both synthetic
and real data but also requires lower computational complexity, making it
suitable to high dimensional settings.
