High-Dimensional Quadratic Discriminant Analysis under Spiked Covariance Model

TL;DR

This paper introduces a new high-dimensional quadratic discriminant analysis method tailored for spiked covariance models, improving classification accuracy and computational efficiency over existing regularized QDA techniques.

Contribution

It proposes a novel quadratic classifier that maximizes the fisher-discriminant ratio specifically for spiked covariance structures, outperforming classical R-QDA in accuracy and efficiency.

Findings

Outperforms classical R-QDA in synthetic and real data

Requires lower computational complexity

Effective in high-dimensional settings

Abstract

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.