Generalized Spherical Principal Component Analysis

TL;DR

This paper introduces a robust generalized spherical PCA method based on the generalized spatial sign covariance matrix, offering improved robustness and efficiency against outliers with low computational cost.

Contribution

It proposes a novel robust PCA technique using the generalized spatial sign covariance matrix, with theoretical analysis and practical improvements for outlier resistance.

Findings

The method exhibits high robustness to outliers.

It maintains good efficiency and low computational cost.

Theoretical properties like influence functions and breakdown values are established.

Abstract

Outliers contaminating data sets are a challenge to statistical estimators. Even a small fraction of outlying observations can heavily influence most classical statistical methods. In this paper we propose generalized spherical principal component analysis, a new robust version of principal component analysis that is based on the generalized spatial sign covariance matrix. Supporting theoretical properties of the proposed method including influence functions, breakdown values and asymptotic efficiencies are studied, and a simulation study is conducted to compare our new method to existing methods. We also propose an adjustment of the generalized spatial sign covariance matrix to achieve better Fisher consistency properties. We illustrate that generalized spherical principal component analysis, depending on a chosen radial function, has both great robustness and efficiency properties in addition to a low computational cost.