2025/10/15 by Hung Hung, Zhi-Yu Jou, Hung, Hung +5
Decision Sciences · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Methodology (stat.ME) #Simulation Techniques and Applications #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2510.13159
openalex publication_date 2025/10/15 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28
Principal component analysis (PCA) is a fundamental tool in multivariate statistics, yet its sensitivity to outliers and limitations in distributed environments restrict its effectiveness in modern large-scale applications. To address these challenges, we introduce the ϕ-PCA framework which provides a unified formulation of robust and distributed PCA. The class of ϕ-PCA methods retains the asymptotic efficiency of standard PCA, while aggregating multiple local estimates using a proper ϕ function enhances ordering-robustness, leading to more accurate eigensubspace estimation under contamination. Notably, the harmonic mean PCA (HM-PCA), corresponding to the choice ϕ(u)=u-1, achieves optimal ordering-robustness and is recommended for practical use. Theoretical results further show that robustness increases with the number of partitions, a phenomenon seldom explored in the literature on robust or distributed PCA. Altogether, the partition-aggregation principle underlying ϕ-PCA offers a general strategy for developing robust and efficiency-preserving methodologies applicable to both robust and distributed data analysis.