A Compressive Classification Framework for High-Dimensional Data

Abstract

We propose a compressive classification framework for settings where the data dimensionality is significantly larger than the sample size. The proposed method, referred to as compressive regularized discriminant analysis (CRDA), is based on linear discriminant analysis and has the ability to select significant features by using joint-sparsity promoting hard thresholding in the discriminant rule. Since the number of features is larger than the sample size, the method also uses state-of-the-art regularized sample covariance matrix estimators. Several analysis examples on real data sets, including image, speech signal and gene expression data illustrate the promising improvements offered by the proposed CRDA classifier in practise. Overall, the proposed method gives fewer misclassification errors than its competitors, while at the same time achieving accurate feature selection results. The open-source R package and MATLAB toolbox of the proposed method (named compressiveRDA) is freely available.

Keywords

• Classification
• covariance matrix estimation
• discriminant analysis
• feature selection
• high-dimensional statistics
• joint-sparse recovery