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