Sparse Functional Singular Value Decomposition for Biclustering and Triclustering Longitudinal Data

2026-06-03

AI Summary

This study addresses the challenge of uncovering disease heterogeneity from high-dimensional, sparse, and irregularly sampled longitudinal omics data. To this end, the authors propose the Tri-SfSVD framework, which, for the first time, simultaneously performs sparse functional biclustering and triclustering across subjects, features, and time domains within a unified optimization model—without requiring data imputation or strong homogeneity assumptions. Built upon sparsity-penalized functional singular value decomposition and enhanced by cross-dimensional regularization, the method consistently outperforms existing approaches in both simulated and real-world datasets. It successfully identifies microbiome pathway–associated subtypes in inflammatory bowel disease (IBD) and reveals spatiotemporal patterns of electroencephalographic (EEG) activity, thereby effectively elucidating latent disease structures.

Abstract

Identifying subtypes of complex conditions, such as Inflammatory Bowel Disease (IBD), often requires capturing latent patterns in longitudinal omics data. However, these data are typically high-dimensional, sparsely sampled, and irregularly observed over time, posing substantial challenges for conventional (bi)clustering and functional data analysis methods. We propose Tri-SfSVD, a unified sparse functional Singular Value Decomposition framework for discovering biclusters and triclusters in longitudinal data. Unlike existing functional biclustering methods that rely on ad hoc imputation or enforce restrictive shape-homogeneity assumptions, Tri-SfSVD integrates continuous trajectory estimation with simultaneous subject, feature, and temporal selection within a single optimization framework. By imposing sparse penalties across subjects, variables, and temporal subregions, the proposed method works directly on observed data to uncover localized structures at the subject, subject-feature, and subject-feature-time levels. Extensive simulations demonstrate that Tri-SfSVD outperforms existing approaches in high-dimensional settings. Applied to IBD multi-omics data, the method identified three biclusters linking sample clusters with distinct IBD-related clinical characteristics to microbial pathway groups associated with specific bacterial taxa, providing interpretable subject-pathway associations for characterizing disease heterogeneity. Applied to multi-channel EEG data, the method identified three triclusters linking sample clusters with distinct alcohol-related phenotypes to localized brain activity patterns, including subgroup differences separated by temporal subregions within the same spatial region.

Problem

• longitudinal data
• biclustering
• triclustering
• sparsity
• high-dimensional data

Innovation

• Sparse Functional SVD
• Biclustering
• Triclustering
• Longitudinal Data
• High-dimensional Omics