A Functional SVD Framework for Regularized Multivariate Functional PCA with Dual Penalization
Abstract
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. This dual-penalization strategy represents a significant advancement beyond existing covariance-based eigen decomposition methods, which penalize only the functional PCs. Two power algorithm implementations, sequential and joint, are proposed, together with a cross-validation approach based on iterative regression for optimal smoothing parameter selection. Comprehensive simulation studies and real data applications demonstrate that the proposed framework substantially improves the extraction of informative and interpretable components, offering methodological and practical benefits for analyzing multivariate functional data across diverse domains.
Related
- A Formal Graphical Inference Framework for Combining Effect Size with Statistical Significance: Application to Multivariate and Functional Linear Models
- Robust Dual-Regularized Variable Selection under Outlier Contamination
- Continuous Dual Maximizers for Fixed-Reference Entropy-Regularized Wasserstein Barycenters
- Fast Rates and Strong Convergence of Tikhonov-Regularized Mixed-Order Primal-Dual Dynamics for Linearly Constrained Optimization Without Eventual Ball Conditions
- Geometric and stochastic framework for a regularized p(x)-Laplacian
BibTeX
@misc{zhao2026functional,
title = {{A Functional SVD Framework for Regularized Multivariate Functional PCA with Dual Penalization}},
author = {Yue Zhao and Hossein Haghbin and Rebecca Sanders and Mehdi Maadooliat},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14815},
eprint = {2609.14815},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14815},
}
RIS
TY - UNPB
TI - A Functional SVD Framework for Regularized Multivariate Functional PCA with Dual Penalization
AU - Yue Zhao
AU - Hossein Haghbin
AU - Rebecca Sanders
AU - Mehdi Maadooliat
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14815
UR - https://arxiv.org/abs/2609.14815
AB - 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. This dual-penalization strategy represents a significant advancement beyond existing covariance-based eigen decomposition methods, which penalize only the functional PCs. Two power algorithm implementations, sequential and joint, are proposed, together with a cross-validation approach based on iterative regression for optimal smoothing parameter selection. Comprehensive simulation studies and real data applications demonstrate that the proposed framework substantially improves the extraction of informative and interpretable components, offering methodological and practical benefits for analyzing multivariate functional data across diverse domains.
ER -