A Time-aware tensor decomposition for tracking evolving patterns

TL;DR

This paper introduces tPARAFAC2, a tensor decomposition method that incorporates temporal regularization to effectively capture evolving patterns in time-series tensor data.

Contribution

The paper proposes a novel tensor factorization approach, tPARAFAC2, that models gradual pattern changes over time, addressing limitations of existing methods.

Findings

tPARAFAC2 outperforms PARAFAC2 and coupled matrix factorization in capturing evolving patterns.

The method accurately models temporal dynamics in synthetic datasets.

Extensive experiments validate the effectiveness of tPARAFAC2.

Abstract

Time-evolving data sets can often be arranged as a higher-order tensor with one of the modes being the time mode. While tensor factorizations have been successfully used to capture the underlying patterns in such higher-order data sets, the temporal aspect is often ignored, allowing for the reordering of time points. In recent studies, temporal regularizers are incorporated in the time mode to tackle this issue. Nevertheless, existing approaches still do not allow underlying patterns to change in time (e.g., spatial changes in the brain, contextual changes in topics). In this paper, we propose temporal PARAFAC2 (tPARAFAC2): a PARAFAC2-based tensor factorization method with temporal regularization to extract gradually evolving patterns from temporal data. Through extensive experiments on synthetic data, we demonstrate that tPARAFAC2 can capture the underlying evolving patterns accurately performing better than PARAFAC2 and coupled matrix factorization with temporal smoothness regularization.