tPARAFAC2: Tracking evolving patterns in (incomplete) temporal data

TL;DR

tPARAFAC2 is a novel tensor factorization method designed to track evolving patterns in temporal data, effectively handling incomplete datasets with improved accuracy over existing techniques.

Contribution

The paper introduces tPARAFAC2, extending existing algorithms to incomplete data, and demonstrates its effectiveness in capturing evolving patterns with noise and missing data.

Findings

tPARAFAC2 outperforms state-of-the-art methods in noisy, incomplete data scenarios.

The method effectively reveals underlying evolving patterns in real datasets.

It handles missing data robustly while maintaining interpretability.

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 the 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. Previously, Alternating Optimization (AO) and Alternating Direction Method of Multipliers (ADMM)-based algorithmic approach has been introduced to fit the PARAFAC2 model to fully observed data. In this paper, we extend this algorithmic framework to the case of partially observed data and use it to fit the tPARAFAC2 model to complete and incomplete datasets with the goal of revealing evolving patterns. Our numerical experiments on simulated datasets demonstrate that tPARAFAC2 can extract the underlying evolving patterns more accurately compared to the state-of-the-art in the presence of high amounts of noise and missing data. Using two real datasets, we also demonstrate the effectiveness of the algorithmic approach in terms of handling missing data and tPARAFAC2 model in terms of revealing evolving patterns. The paper provides an extensive comparison of different approaches for handling missing data within the proposed framework, and discusses both the advantages and limitations of tPARAFAC2 model.