Highly Robust Classification: A Regularized Approach for Omics Data

Abstract

Various regularized approaches to linear discriminant analysis suffer from sensitivity to the presence of outlying measurements in the data. This work has the aim to propose new versions of regularized linear discriminant analysis suitable for high-dimensional data contaminated by outliers. We use principles of robust statistics to propose classification methods suitable for data with the number of variables exceeding the number of observations. Particularly, we propose two robust regularized versions of linear discriminant analysis, which have a high breakdown point. For this purpose, we propose a regularized version of the minimum weighted covariance determinant estimator, which is one of highly robust estimators of multivariate location and scatter. It assigns implicit weights to individual observations and represents a unique attempt to combine regularization and high robustness. Algorithms for the efficient computation of the new classification methods are proposed and the performance of these methods is illustrated on real data sets.