August 2026 • 1st KDD workshop on Interplay of Classical Tensor Methods and Foundation Models • Jeju, Korea

Temporal multivariate data is ubiquitous in many domains, collected over time at planned visits in longitudinal cohorts or at specific intervals in challenge tests. While the analysis of such data often focuses on revealing temporal patterns common across subjects, subject-specific differences in those patterns hold the promise to enhance our understanding of underlying mechanisms and facilitate personalized approaches. However, reliably extracting such temporal patterns from longitudinal multivariate data remains an open challenge. In this work, we demonstrate that coupled matrix factorizations (CMF) and PARAFAC2 are effective tools for capturing such subject-specific temporal profiles, focusing on two novel applications. In longitudinal metabolomics, CMF and PARAFAC2 reveal differences in postprandial metabolic responses of individuals according to body mass index (BMI) and insulin resistance (IR) measures. In sensitization data analysis, both methods capture differences in temporal trajectories of children according to delivery mode, insights that CANDECOMP/PARAFAC (CP), the current state of the art, fails to uncover. We also demonstrate the reproducibility and replicability of the extracted patterns. This is joint work with David Horner, Rasmus Bro, Ann-Marie M Schoos, Morten Arendt Rasmussen and Evrim Acar.

July 2026 • Greeks in AI 2026 • Athens, Greece

**Motivation:** Temporal 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. **Results:** We 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. This is joint work with David Horner, Rasmus Bro, Ann-Marie M Schoos, Morten Arendt Rasmussen and Evrim Acar.

June 2025 • TRICAP (Three-way Methods in Chemistry and Psychology) 2025 • Ålesund, Norway

In this talk, we discuss why existing works might be unsuitable for the task of analyzing time-evolving data and introduce two time-aware methods: t(emporal)PARAFAC and d(ynamical)CMF. With extensive synthetic experiments we compare these methods with the state-of-the-art for the task of uncovering evolving patterns in terms of accuracy, while also highlighting the benefits and limitations with respect to the three essential requirements of analyzing temporal data: (a) time-awareness, (b) structural flexibility, and (c) uniqueness. This is joint work with Carla Schenker, Max Pfeffer, Pedro Lind, Jérémy E. Cohen and Evrim Acar.