A1903
Title: Globally aligned principal component analysis for multi-group data
Authors: Hedayat Fathi - Universite Laval (Canada)
Marzia Cremona - Universite Laval (Canada)
Federico Severino - Universite Laval (Canada) [presenting]
Abstract: A novel principal component analysis (PCA) method for multi-group datasets is proposed, where multiple numerical variables are measured across different groups. The method combines group-specific principal components with global ones through an explicit alignment mechanism based on regularized optimization. A globally aligned covariance matrix is introduced that incorporates weighted contributions from global principal directions, balancing the preservation of within-group variance with global coherence. The alignment strength is controlled by regularization parameters that can be tuned to achieve the desired trade-off. A comprehensive simulation study demonstrates that the aligned approach achieves a favorable compromise between capturing local variation within groups and maintaining interpretability and stability across groups. The method addresses an important gap in the PCA literature, as existing approaches either ignore group structure entirely, focus exclusively on local structure through group-wise PCA, or impose restrictive assumptions of common principal components. The proposed approach respects the multi-group nature of data while improving global comparability of components. An application to 2021 Canadian Census socioeconomic data demonstrates that the proposed alignment yields more comparable and stable region-specific components than pooled or purely region-wise PCA.
