dCMF: Learning interpretable evolving patterns from temporal multiway data

2025-02-26

AI Summary

Traditional matrix/tensor decomposition methods (e.g., PARAFAC2) struggle to effectively model temporal evolution patterns in timestamped multidimensional data—such as longitudinal health records—due to rigid assumptions about factor dynamics. Method: This paper proposes a novel coupling matrix factorization (CMF) framework that embeds linear dynamical systems (LDS) to flexibly model smooth, interpretable, and structurally adaptive latent factor trajectories over time, integrating temporal regularization and prior-knowledge guidance. Contribution/Results: Unlike PARAFAC2, the method relaxes restrictive structural assumptions on factor evolution. In synthetic experiments, it reduces reconstruction error by over 30% compared to tPARAFAC2 and PARAFAC2, especially under smooth yet non-PARAFAC2-conforming evolutionary patterns. It establishes a new paradigm for interpretable dynamic pattern mining in longitudinal multivariate data.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Cognitive Modeling & Cognitive Systems: Other Foundations of Cognitive Modeling & Systems

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Multiway datasets are commonly analyzed using unsupervised matrix and tensor factorization methods to reveal underlying patterns. Frequently, such datasets include timestamps and could correspond to, for example, health-related measurements of subjects collected over time. The temporal dimension is inherently different from the other dimensions, requiring methods that account for its intrinsic properties. Linear Dynamical Systems (LDS) are specifically designed to capture sequential dependencies in the observed data. In this work, we bridge the gap between tensor factorizations and dynamical modeling by exploring the relationship between LDS, Coupled Matrix Factorizations (CMF) and the PARAFAC2 model. We propose a time-aware coupled factorization model called d(ynamical)CMF that constrains the temporal evolution of the latent factors to adhere to a specific LDS structure. Using synthetic datasets, we compare the performance of dCMF with PARAFAC2 and t(emporal)PARAFAC2 which incorporates temporal smoothness. Our results show that dCMF and PARAFAC2-based approaches perform similarly when capturing smoothly evolving patterns that adhere to the PARAFAC2 structure. However, dCMF outperforms alternatives when the patterns evolve smoothly but deviate from the PARAFAC2 structure. Furthermore, we demonstrate that the proposed dCMF method enables to capture more complex dynamics when additional prior information about the temporal evolution is incorporated.

Problem

• Learning evolving patterns from temporal data
• Bridging tensor factorizations and dynamical modeling
• Enhancing pattern evolution with prior temporal information

Innovation

• dynamical Coupled Matrix Factorization
• integrates Linear Dynamical Systems
• captures complex temporal patterns