Chatzis, C. | Search bioRxiv

bioRxiv2026

Revealing Subject-Specific Temporal Patterns from Longitudinal Data

MotivationTemporal multivariate data is ubiquitous in many domains, for instance, being collected over time at planned visits (every few months/years) in longitudinal cohorts, or every few minutes/hours in challenge tests. The analysis of such data often focuses on revealing the underlying temporal patterns common across subjects. However, there are subject-specific differences in temporal patterns, which hold the promise to enhance our understanding of underlying mechanisms and facilitate personalized approaches. Nevertheless, extracting subject-specific temporal patterns from longitudinal multivariate data reliably is an open challenge. ResultsWe introduce coupled matrix factorizations (CMF) as effective tools to capture subject-specific temporal patterns focusing on two novel applications: analysis of longitudinal metabolomics data and sensitization data. Our analysis shows that CMF models reliably capture subject-specific (shape) differences in temporal patterns revealing further in-sights compared to the state of the art. In metabolomics, CMF models reveal differences in metabolic responses of individuals (in a postprandial meal challenge) according to anthropometric and insulin sensitivity measures. In sensitization data analysis, CMF-based methods capture differences in temporal trajectories of children according to delivery/birth mode. We demonstrate the reliability of extracted patterns using reproducibility and replicability. AvailabilityThe code is available on https://github.com/cchatzis/Revealing-Subject-specific-Temporal-Patterns-from-Longitudinal-Data. Clinical data is not publicly available due to privacy reasons. Data can be made available under a joint research collaboration by contacting COPSAC (administration@dbac.dk).

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bioRxiv2025

Extracting host-specific developmental signatures from longitudinal microbiome data

Longitudinal microbiome studies provide critical insights into microbial community dynamics and their relation to host health. Tensor decompositions offer a powerful framework for the unsupervised analysis of such data, yielding interpretable low-dimensional temporal patterns. However, existing approaches based on the CANDECOMP/PARAFAC (CP) model assume common temporal dynamics for all subjects and therefore cannot capture subject-specific trajectories. To address this limitation, we introduce a novel analytical framework based on PARAFAC2 to explicitly model subject-specific variations, such as shifts and delays in temporal patterns. Through systematic comparisons on simulated and real-world datasets--including studies of infant gut maturation and dietary interventions--we demonstrate that PARAFAC2 outperforms CP in capturing subject-specific temporal trajectories, and enables the discovery of biologically relevant patterns that are overlooked by CP. Furthermore, we introduce replicability as a robust criterion for selecting the number of components and demonstrate that the extracted patterns are replicable. Author summaryLongitudinal microbiome datasets are complex, consisting of repeated high-dimensional compositions that track changes in microbial abundance across individuals over time. While tensor decompositions are powerful tools for unraveling structure in these data, standard models like CANDECOMP/PARAFAC (CP) impose a critical limitation: they assume that temporal dynamics are identical across all individuals. This assumption often fails to capture the heterogeneity of biological processes, such as the varying pace of gut microbiome maturation or distinct individual responses to dietary changes. In this work, we introduce a novel analytical framework leveraging the PARAFAC2 model to overcome these constraints. By explicitly modeling subject-specific temporal variations, our PARAFAC2-based approach allows for the detection of individual time shifts and delays. We validated this framework using both simulation and real-world cohorts, demonstrating its ability to recover personalized trajectories that CP obscures. Additionally, we implemented a robust criterion to guide model selection, ensuring that the discovered patterns are replicable.

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