On Coupling Robust Estimation with Regularization for High-Dimensional Data

Standard data mining procedures are sensitive to the presence of outlying measurements in the data. Therefore, robust data mining procedures are highly desirable, which are resistant to outliers. This work has the aim to propose new robust classification procedures for high-dimensional data and algorithms for their efficient computation. Particularly, we use the idea of implicit weights assigned to individual observation to propose several robust regularized versions of linear discriminant analysis (LDA), suitable for data with the number of variables exceeding the number of observations. The approach is based on a regularized version of the minimum weighted covariance determinant (MWCD) estimator and represents a unique attempt to combine regularization and high robustness, allowing to down-weight outlying observations. Classification performance of new methods is illustrated on real fMRI data acquired in neuroscience research.