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 bi-
clustering methods that rely on ad hoc imputation or enforce restrictive shape-homogeneity
assumptions, Tri-SfSVD integrates continuous trajectory estimation with simultaneous sub-
ject, 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, includ-
ing subgroup differences separated by temporal subregions within the same spatial region.