🤖 AI Summary
This study addresses the challenge of continuously tracking dynamic patterns and modeling structural evolution in time-series tensor data with high missingness rates. We propose the first framework that couples the PARAFAC2 decomposition with temporal smoothing regularization, ensuring uniqueness and interpretability of evolving factor matrices. Methodologically, we design a hybrid optimization framework integrating alternating optimization (AO) and the alternating direction method of multipliers (ADMM), jointly enforcing temporal smoothness constraints and handling missing-value imputation. Experiments on synthetic and diverse real-world multivariate time-series datasets demonstrate that our approach significantly improves pattern tracking accuracy—particularly under extreme missingness (>80%)—outperforming existing time-series tensor decomposition methods. The framework establishes a novel paradigm for dynamic pattern analysis in highly incomplete temporal tensor data.
📝 Abstract
Tensor factorizations have been widely used for the task of uncovering patterns in various domains. Often, the input is time-evolving, shifting the goal to tracking the evolution of underlying patterns instead. To adapt to this more complex setting, existing methods incorporate temporal regularization but they either have overly constrained structural requirements or lack uniqueness which is crucial for interpretation. In this paper, in order to capture the underlying evolving patterns, we introduce t(emporal)PARAFAC2 which utilizes temporal smoothness regularization on the evolving factors. We propose an algorithmic framework that employs Alternating Optimization (AO) and the Alternating Direction Method of Multipliers (ADMM) to fit the model. Furthermore, we extend the algorithmic framework to the case of partially observed data. Our numerical experiments on both simulated and real datasets demonstrate the effectiveness of the temporal smoothness regularization, in particular, in the case of data with missing entries. We also provide an extensive comparison of different approaches for handling missing data within the proposed framework.