提出dCMF模型，用动态系统建模时序多维数据的演化模式。
dCMF: Learning interpretable evolving patterns from temporal multiway data
- 将线性动态系统融入耦合矩阵分解，约束潜在因子随时间演化。
- 在非PARAFAC2结构下，dCMF比PARAFAC2和tPARAFAC2更优。
- 适合有时间演化先验知识的时序多维数据分析场景。
多维数据常通过无监督矩阵与张量分解揭示潜在模式。这类数据常含时间戳，如随时间采集的健康指标。时间维度具有特殊性，需考虑其内在特性。线性动态系统（LDS）专为捕捉序列依赖设计。本文连接张量分解与动态建模，探索LDS、耦合矩阵分解（CMF）与PARAFAC2之间的关系。提出一种时序感知的耦合分解模型dCMF，强制潜变量的时间演化符合特定LDS结构。通过合成数据对比dCMF与PARAFAC2及引入时间平滑性的tPARAFAC2，结果表明：当模式符合PARAFAC2结构时，两者性能相当；但当模式平滑演化却偏离该结构时，dCMF表现更优。此外，当加入关于时间演化的额外先验信息时，dCMF可捕捉更复杂动态。
原文摘要 · Abstract (English)
Multiway datasets are commonly analyzed using unsupervised matrix and tensor factorization methods to reveal underlying patterns. Frequently, such datasets include timestamps and could correspond to, for example, health-related measurements of subjects collected over time. The temporal dimension is inherently different from the other dimensions, requiring methods that account for its intrinsic properties. Linear Dynamical Systems (LDS) are specifically designed to capture sequential dependencies in the observed data. In this work, we bridge the gap between tensor factorizations and dynamical modeling by exploring the relationship between LDS, Coupled Matrix Factorizations (CMF) and the PARAFAC2 model. We propose a time-aware coupled factorization model called d(ynamical)CMF that constrains the temporal evolution of the latent factors to adhere to a specific LDS structure. Using synthetic datasets, we compare the performance of dCMF with PARAFAC2 and t(emporal)PARAFAC2 which incorporates temporal smoothness. Our results show that dCMF and PARAFAC2-based approaches perform similarly when capturing smoothly evolving patterns that adhere to the PARAFAC2 structure. However, dCMF outperforms alternatives when the patterns evolve smoothly but deviate from the PARAFAC2 structure. Furthermore, we demonstrate that the proposed dCMF method enables to capture more complex dynamics when additional prior information about the temporal evolution is incorporated.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。