Fast computation of robust subspace estimators

Abstract

Dimension reduction is often an important step in the analysis of high-dimensional data. PCA is a popular technique to find the best low-dimensional approximation of high-dimensional data. However, classical PCA is very sensitive to atypical data. Robust methods to estimate the low-dimensional subspace that best approximates the regular data have been proposed by Maronna (2005). However, for high-dimensional data his algorithms become computationally expensive. Alternative algorithms for the robust subspace estimators are proposed that are better suited to compute the solution for high-dimensional problems. The main ingredients of the new algorithms are twofold. First, the principal directions of the subspace are estimated directly by iterating the estimating equations corresponding to the estimators. Second, to reduce computation time even further five robust deterministic values are proposed to initialize the algorithms instead of using random starting values. It is shown that the new algorithms yield robust solutions and the computation time is largely reduced, especially for high-dimensional data.