Modal Principal Component Analysis

TL;DR

This paper introduces Modal PCA, a robust dimension reduction technique based on mode estimation, which improves outlier resistance over traditional PCA, supported by theoretical analysis and experimental validation.

Contribution

It proposes a novel MPCA method utilizing mode estimation for robustness, with theoretical properties and empirical advantages demonstrated.

Findings

MPCA effectively resists outliers compared to standard PCA.

Theoretical properties such as convergence and breakdown point are established.

Experimental results show MPCA's superior performance in practical scenarios.

Abstract

Principal component analysis (PCA) is a widely used method for data processing, such as for dimension reduction and visualization. Standard PCA is known to be sensitive to outliers, and thus, various robust PCA methods have been proposed. It has been shown that the robustness of many statistical methods can be improved using mode estimation instead of mean estimation, because mode estimation is not significantly affected by the presence of outliers. Thus, this study proposes a modal principal component analysis (MPCA), which is a robust PCA method based on mode estimation. The proposed method finds the minor component by estimating the mode of the projected data points. As theoretical contribution, probabilistic convergence property, influence function, finite-sample breakdown point and its lower bound for the proposed MPCA are derived. The experimental results show that the proposed method has advantages over the conventional methods.