Fast Computation of Robust Subspace Estimators

TL;DR

This paper introduces efficient algorithms for robust subspace estimation in high-dimensional data, significantly reducing computation time while maintaining robustness against atypical data points.

Contribution

The paper proposes novel algorithms that directly estimate principal directions and use deterministic initializations, improving computational efficiency for high-dimensional robust subspace estimation.

Findings

Algorithms are faster than existing methods for high-dimensional data.

Robust solutions are achieved without sacrificing accuracy.

Deterministic initializations improve convergence speed.

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. 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.