{"ID":3084713,"CreatedAt":"2026-06-05T06:46:15.197025399Z","UpdatedAt":"2026-06-06T21:45:49.600566077Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.05488","arxiv_id":"2606.05488","title":"Sparse Functional Singular Value Decomposition for Biclustering and Triclustering Longitudinal Data","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.","short_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)clusteri...","url_abs":"https://arxiv.org/abs/2606.05488","url_pdf":"https://arxiv.org/pdf/2606.05488v1","authors":"[\"Yue Zhao\",\"Thierry Chekouo\",\"Sandra Safo\"]","published":"2026-06-03T22:26:01Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"stat.ME\"]","methods":"[]","has_code":false}