dCMF: Learning interpretable evolving patterns from temporal multiway data
This work addresses the need for interpretable temporal pattern analysis in domains like health monitoring, though it appears incremental by combining existing tensor and dynamical modeling approaches.
The authors tackled the problem of analyzing temporal multiway data by proposing dCMF, a time-aware coupled factorization model that integrates tensor factorizations with linear dynamical systems to capture evolving patterns; results showed dCMF performs similarly to PARAFAC2-based methods for smoothly evolving patterns adhering to PARAFAC2 structure but outperforms them when patterns deviate from this structure.
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.