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A Functional SVD Framework for Regularized Multivariate Functional PCA with Dual Penalization

arXiv · AI, language, vision and robotics · article · Sep 13, 2026 · UTC

This paper introduces a novel framework for Regularized Multivariate Functional Principal Component Analysis (ReMFPCA) via Functional Singular Value Decomposition (SVD). The proposed method extends existing MFPCA approaches by incorporating a generalized functional SVD within a Hilbert space framework, enabling simultaneous regularization of both functional principal components (PCs) and their associated PC scores. A key innovation of this framework is the inclusion of a sparsity penalty on the PC scores, which enhances interpretability by filtering out irrelevant subject-specific variations.

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