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.

翻译：时间演化数据集通常可以排列为一个高阶张量，其中时间作为其中一个模式。尽管张量分解已成功用于捕捉此类高阶数据集中的潜在模式，但时间维度往往被忽略，从而允许时间点的重新排序。在近期研究中，时间正则化项被引入时间模式以解决该问题。然而，现有方法仍不允许潜在模式随时间变化（例如，大脑中的空间变化、主题的语境变化）。本文提出时间PARAFAC2（tPARAFAC2）：一种基于PARAFAC2的张量分解方法，通过引入时间正则化从时间数据中提取渐进演化模式。通过在合成数据上的广泛实验，我们证明tPARAFAC2能够准确捕捉潜在的演化模式，其性能优于PARAFAC2以及带有时间平滑正则化的耦合矩阵分解方法。