发表机构
University of Minnesota; Persian Gulf University; Marquette University（明尼苏达大学; 波斯湾大学; 马凯特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于函数奇异值分解的正则化多元函数主成分分析框架，通过双惩罚同时正则化主成分及得分，增强可解释性，并借助幂算法与交叉验证提升提取效果。
AI 中文摘要
本文通过函数奇异值分解（SVD）引入了一种用于正则化多元函数主成分分析（ReMFPCA）的新框架。所提出的方法通过在希尔伯特空间框架内纳入广义函数奇异值分解，扩展了现有的MFPCA方法，从而能够同时正则化函数主成分（PCs）及其相关的PC得分。该框架的一个关键创新是包含了对PC得分的稀疏性惩罚，通过过滤掉不相关的个体特定变异来增强可解释性。这种双惩罚策略代表了超越现有基于协方差的本征分解方法的重要进步，后者仅对函数主成分进行惩罚。提出了两种幂算法实现，即顺序和联合，以及一种基于迭代回归的交叉验证方法，用于最优平滑参数选择。全面的模拟研究和真实数据应用表明，所提出的框架显著提高了对信息丰富且可解释成分的提取，为跨多个领域分析多元函数数据提供了方法论和实践上的益处。
英文摘要
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.
