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：时变数据集通常可以组织为高阶张量，其中时间模式作为其中一个维度。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视，从而允许时间点的重新排列。近年来的研究通过在时间模式中引入时间正则化来解决这一问题。然而，现有方法仍无法支持潜在模式随时间变化（例如，大脑中的空间变化、主题的上下文变化）。本文提出时间PARAFAC2（tPARAFAC2）：一种基于PARAFAC2的张量分解方法，结合时间正则化从时间数据中提取逐渐演化的模式。通过对合成数据的广泛实验，我们证明tPARAFAC2能够准确捕捉潜在的演化模式，其表现优于PARAFAC2以及带有时间平滑正则化的耦合矩阵分解方法。