A Time-aware tensor decomposition for tracking evolving patterns
This work addresses the need for better modeling of gradually changing patterns in temporal data, such as in brain imaging or topic analysis, representing an incremental improvement over prior tensor factorization approaches.
The paper tackles the problem of capturing evolving patterns in time-evolving tensor data by proposing tPARAFAC2, a method that incorporates temporal regularization into PARAFAC2-based factorization, and demonstrates through experiments on synthetic data that it accurately captures evolving patterns and outperforms existing methods like PARAFAC2 and coupled matrix factorization with temporal smoothness regularization.
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.