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

arXiv: https://arxiv.org/abs/2609.14815 · HTML: https://mlsanity.com/paper/2609.14815/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 30 references that are in the map.
- First posted on arXiv 13 Sep 2026.

## Builds on (most cited first, 6 of 6)

- [Mobile Sensor Data Anonymization](https://mlsanity.com/paper/1810.11546/) (2018)
- [Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains](https://mlsanity.com/paper/1509.02029/) (2015)
- [Sparse and Functional Principal Components Analysis](https://mlsanity.com/paper/1309.2895/) (2013)
- [Localized Functional Principal Component Analysis](https://mlsanity.com/paper/1501.04933/) (2015)
- [Functional Singular Spectrum Analysis](https://mlsanity.com/paper/1906.05232/) (2019)
- [Regularized Multivariate Functional Principal Component Analysis](https://mlsanity.com/paper/2306.13980/) (2023)

## Abstract (arXiv)

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.