MacroPCA: An all-in-one PCA method allowing for missing values as well as cellwise and rowwise outliers

TL;DR

MacroPCA is a novel PCA method that simultaneously handles missing data, cellwise outliers, and rowwise outliers, providing a robust and versatile tool for multivariate data analysis.

Contribution

It introduces the first PCA approach capable of managing missing values, cellwise outliers, and rowwise outliers all at once, combining strengths of existing robust methods.

Findings

MacroPCA effectively detects outliers in complex data.

The method maintains robustness with high proportions of contaminated cells.

It is suitable for online process control applications.

Abstract

Multivariate data are typically represented by a rectangular matrix (table) in which the rows are the objects (cases) and the columns are the variables (measurements). When there are many variables one often reduces the dimension by principal component analysis (PCA), which in its basic form is not robust to outliers. Much research has focused on handling rowwise outliers, i.e. rows that deviate from the majority of the rows in the data (for instance, they might belong to a different population). In recent years also cellwise outliers are receiving attention. These are suspicious cells (entries) that can occur anywhere in the table. Even a relatively small proportion of outlying cells can contaminate over half the rows, which causes rowwise robust methods to break down. In this paper a new PCA method is constructed which combines the strengths of two existing robust methods in order to be robust against both cellwise and rowwise outliers. At the same time, the algorithm can cope with missing values. As of yet it is the only PCA method that can deal with all three problems simultaneously. Its name MacroPCA stands for PCA allowing for Missingness And Cellwise & Rowwise Outliers. Several simulations and real data sets illustrate its robustness. New residual maps are introduced, which help to determine which variables are responsible for the outlying behavior. The method is well-suited for online process control.