PARAFAC2 has demonstrated success in modeling irregular tensors, where the tensor dimensions vary across one of the modes. An example scenario is jointly modeling treatments across a set of patients with varying number of medical encounters, where the alignment of events in time bears no clinical meaning, and it may also be impossible to align them due to their varying length. Despite recent improvements on scaling up unconstrained PARAFAC2, its model factors are usually dense and sensitive to noise which limits their interpretability. As a result, the following open challenges remain: a) various modeling constraints, such as temporal smoothness, sparsity and non-negativity, are needed to be imposed for interpretable temporal modeling and b) a scalable approach is required to support those constraints efficiently for large datasets. To tackle these challenges, we propose a COnstrained PARAFAC2 (COPA) method, which carefully incorporates optimization constraints such as temporal smoothness, sparsity, and non-negativity in the resulting factors. To efficiently support all those constraints, COPA adopts a hybrid optimization framework using alternating optimization and alternating direction method of multiplier (AO-ADMM). As evaluated on large electronic health record (EHR) datasets with hundreds of thousands of patients, COPA achieves significant speedups (up to 36x faster) over prior PARAFAC2 approaches that only attempt to handle a subset of the constraints that COPA enables. Overall, our method outperforms all the baselines attempting to handle a subset of the constraints in terms of speed, while achieving the same level of accuracy.

本研究提出了一种基于协同优化和单向距离方法（AO-ADMM）的新的COPA方法，该方法的目的是解决PARAFAC2模型的因子分解在应对时空约束时的可解释性不足和噪声敏感性等问题。通过实验，COA方法比以前的PARAFAC2方法更快，并取得了与在精度方面与前者相同的表现。

COPA: 用于稀疏和大型数据集的约束PARAFAC2