Cellwise Robust Twoblock Dimension Reduction

2026-04-16

AI Summary

This study addresses the challenge that traditional robust methods struggle with contamination scattered across individual cells in multivariate data. The authors propose a cell-wise robust two-block dimension reduction approach that identifies anomalous cells through column-wise prescreening and performs model-driven imputation within an iteratively reweighted M-estimation framework, thereby preserving useful information from partially contaminated rows. This method is the first to achieve joint robust dimension reduction for both predictor and response blocks in a multivariate setting, supporting both dense and sparse variable selection. It maintains high robustness and efficiency even when more than 50% of the rows contain contaminated cells. Empirical results demonstrate its ability to accurately recover the true outlier structure and informative variable sets, yielding highly interpretable outcomes in real-world applications.

Technology Category

• Machine Learning: Dimensionality Reduction/Feature Selection
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Intelligent Robots: State Estimation

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Cellwise Robust Twoblock (CRTB) is introduced, the first cellwise robust method for simultaneous dimension reduction of multivariate predictor and response blocks, in both a dense and a sparse variable-selecting variant. Classical robust methods protect against casewise outliers by downweighting or removing entire observations, a strategy that becomes inefficient -- and eventually breaks down -- when contamination is scattered across individual cells rather than concentrated in whole rows. CRTB combines a column-wise pre-filter for cellwise outlier detection with model-based imputation of flagged cells inside an iteratively reweighted M-estimation loop, retaining the clean cells of partially contaminated rows instead of discarding the observation. An efficient algorithm is provided that uses the classical twoblock SVD as a warm start and converges in a handful of IRLS iterations at a moderate computational cost. The method resists settings where more than $50\%$ of rows contain contaminated cells while retaining comparable efficiency on clean data. A simulation study confirms these properties and shows that CRTB additionally recovers the underlying cellwise outlier pattern with high fidelity and, in the sparse setting, the correct set of informative variables. Two compelling examples illustrate CRTB's practical utility. In each of these, CRTB is shown to be conducive to results that are highly interpretable in the respective domains in the presence of cellwise outliers. As a by-product, the corresponding cells are identified with high fidelity.

Problem

• cellwise outliers
• dimension reduction
• robust statistics
• multivariate data
• outlier detection

Innovation

• cellwise robustness
• twoblock dimension reduction
• iteratively reweighted M-estimation
• model-based imputation
• sparse variable selection