A note on sensitivity of principal component subspaces and the efficient detection of influential observations in high dimensions

TL;DR

This paper introduces a new influence measure based on second order expansion of RV and GCD metrics, enabling efficient detection of influential observations in high-dimensional principal component analysis.

Contribution

It proposes a novel influence measure for eigenvector perturbation analysis and demonstrates its practical utility in identifying influential data points efficiently.

Findings

The influence measure accurately detects influential observations.

Sample-based implementation is computationally efficient.

The method complements existing influence analysis techniques.

Abstract

In this paper we introduce an influence measure based on second order expansion of the RV and GCD measures for the comparison between unperturbed and perturbed eigenvectors of a symmetric matrix estimator. Example estimators are considered to highlight how this measure compliments recent influence analysis. Importantly, we also show how a sample based version of this measure can be used to accurately and efficiently detect influential observations in practice.