Regularized Multivariate Functional Principal Component Analysis for Data Observed on Different Domains

Authors

Hossein Haghbin, Persian Gulf University
Yue Zhao, Marquette University
Mehdi Maadooliat, Marquette UniversityFollow

Document Type

Article

Publication Date

2026

Publisher

American Institute of Mathematical Sciences

Source Publication

Foundations of Data Science

Source ISSN

2639-8001

Abstract

Multivariate Functional Principal Component Analysis (MFPCA) is a valuable tool for exploring relationships and identifying shared patterns of variation in multivariate functional data. However, controlling the roughness of the extracted Principal Components (PCs) can be challenging. This paper introduces a novel approach called regularized MFPCA (ReMFPCA) to address this issue and enhance the smoothness and interpretability of the multivariate functional PCs. ReMFPCA incorporates a roughness penalty within a penalized framework, using a parameter vector to regulate the smoothness of each functional variable. The proposed method focuses on multivariate functional data on different domains and generates smoothed multivariate functional PCs, providing a concise and interpretable representation of the data. Extensive simulations and real data examples demonstrate the effectiveness of ReMFPCA and its superiority over alternative methods. The proposed approach opens new avenues for analyzing and uncovering relationships in complex multivariate functional datasets.

Comments

Accepted version. Foundations of Data Science, Vol. 10 (2026): 27-52. DOI. © 2026 American Institute of Mathematical Sciences. Used with permission.

Recommended Citation

Haghbin, Hossein; Zhao, Yue; and Maadooliat, Mehdi, "Regularized Multivariate Functional Principal Component Analysis for Data Observed on Different Domains" (2026). Mathematical and Statistical Science Faculty Research and Publications. 164.
https://epublications.marquette.edu/math_fac/164