{"ID":2854981,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.13159","arxiv_id":"2510.13159","title":"The $φ$-PCA Framework: A Unified and Efficiency-Preserving Approach with Robust Variants","abstract":"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.","short_abstract":"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 formula...","url_abs":"https://arxiv.org/abs/2510.13159","url_pdf":"https://arxiv.org/pdf/2510.13159v1","authors":"[\"Hung Hung\",\"Zhi-Yu Jou\",\"Su-Yun Huang\",\"Shinto Eguchi\"]","published":"2025-10-15T05:21:11Z","proceeding":"stat.ME","tasks":"[\"stat.ME\",\"math.ST\",\"stat.ML\"]","methods":"[]","has_code":false}