A Compressive Classification Framework for High-Dimensional Data

We propose a compressive classification framework for settings where the data dimensionality is significantly higher 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.

Sequential adaptive elastic net approach for single-snapshot source localization

This paper proposes efficient algorithms for accurate recovery of direction-of-arrival (DoA) of sources from single-snapshot measurements using compressed beamforming (CBF). In CBF, the conventional sensor array signal model is cast as an underdetermined complex-valued linear regression model and sparse signal recovery methods are used for solving the DoA finding problem. We develop a complex-valued pathwise weighted elastic net (c-PW-WEN) algorithm that finds solutions at knots of penalty parameter values over a path (or grid) of EN tuning parameter values. c-PW-WEN also computes Lasso or weighted Lasso in its path. We then propose a sequential adaptive EN (SAEN) method that is based on c-PW-WEN algorithm with adaptive weights that depend on the previous solution. Extensive simulation studies illustrate that SAEN improves the probability of exact recovery of true support compared to conventional sparse signal recovery approaches such as Lasso, elastic net or orthogonal matching pursuit in several challenging multiple target scenarios. The effectiveness of SAEN is more pronounced in the presence of high mutual coherence.

Compressive Regularized Discriminant Analysis of High-Dimensional Data with Applications to Microarray Studies

We propose a modification of linear discriminant analysis, referred to as compressive regularized discriminant analysis (CRDA), for analysis of high-dimensional datasets. CRDA is specially designed for feature elimination purpose and can be used as gene selection method in microarray studies. CRDA lends ideas from $\ell_{q,1}$ norm minimization algorithms in the multiple measurement vectors (MMV) model and utilizes joint-sparsity promoting hard thresholding for feature elimination. A regularization of the sample covariance matrix is also needed as we consider the challenging scenario where the number of features (variables) is comparable or exceeding the sample size of the training dataset. A simulation study and four examples of real-life microarray datasets evaluate the performances of CRDA based classifiers. Overall, the proposed method gives fewer misclassification errors than its competitors, while at the same time achieving accurate feature selection.