Robust Principal Components by Casewise and Cellwise Weighting

TL;DR

This paper introduces cellPCA, a robust PCA method that effectively handles casewise and cellwise outliers, as well as missing data, using a combined loss function and IRLS algorithm, with demonstrated superior performance.

Contribution

The paper proposes a novel robust PCA approach, cellPCA, capable of simultaneously addressing casewise outliers, cellwise outliers, and missing data within a unified framework.

Findings

CellPCA effectively detects outliers using residual cellmaps.

It outperforms traditional PCA in contaminated data scenarios.

The method is validated through simulations and real data examples.

Abstract

Principal component analysis (PCA) is a fundamental tool for analyzing multivariate data. Here the focus is on dimension reduction to the principal subspace, characterized by its projection matrix. The classical principal subspace can be strongly affected by the presence of outliers. Traditional robust approaches consider casewise outliers, that is, cases generated by an unspecified outlier distribution that differs from that of the clean cases. But there may also be cellwise outliers, which are suspicious entries that can occur anywhere in the data matrix. Another common issue is that some cells may be missing. This paper proposes a new robust PCA method, called cellPCA, that can simultaneously deal with casewise outliers, cellwise outliers, and missing cells. Its single objective function combines two robust loss functions, that together mitigate the effect of casewise and cellwise outliers. The objective function is minimized by an iteratively reweighted least squares (IRLS) algorithm. Residual cellmaps and enhanced outlier maps are proposed for outlier detection. The casewise and cellwise influence functions of the principal subspace are derived, and its asymptotic distribution is obtained. Extensive simulations and two real data examples illustrate the performance of cellPCA.