PARAFAC2 AO-ADMM：所有模式下的约束
PARAFAC2 AO-ADMM: Constraints in all modes
AI总结：
针对PARAFAC2模型演化模式难以正则化的问题，提出基于ADMM的拟合算法，支持任意可近端惩罚，实验证明其准确、高效且约束灵活。
摘要：
PARAFAC2模型为流行的张量分解模型CANDECOMP/PARAFAC（CP）提供了一种灵活的替代方案。与CP不同，PARAFAC2允许一个模式（即演化模式）中的因子矩阵随张量切片而变化，这已被证明在化学计量学和神经科学等不同领域的应用中非常有用。然而，PARAFAC2模型的演化模式传统上是隐式建模的，这使得对其进行正则化具有挑战性。目前，对该模式应用正则化的唯一方法是使用灵活的耦合方法，该方法通过正则化最小二乘子问题求解。在这项工作中，我们转而提出一种基于交替方向乘子法（ADMM）的算法来拟合PARAFAC2，并将可能的正则化惩罚扩展到任何可近端函数。我们的数值实验表明，所提出的基于ADMM的PARAFAC2方法能够从模拟数据中准确恢复潜在成分，同时在施加约束方面既计算高效又灵活。
英文摘要：
The PARAFAC2 model provides a flexible alternative to the popular CANDECOMP/PARAFAC (CP) model for tensor decompositions. Unlike CP, PARAFAC2 allows factor matrices in one mode (i.e., evolving mode) to change across tensor slices, which has proven useful for applications in different domains such as chemometrics, and neuroscience. However, the evolving mode of the PARAFAC2 model is traditionally modelled implicitly, which makes it challenging to regularise it. Currently, the only way to apply regularisation on that mode is with a flexible coupling approach, which finds the solution through regularised least-squares subproblems. In this work, we instead propose an alternating direction method of multipliers (ADMM)-based algorithm for fitting PARAFAC2 and widen the possible regularisation penalties to any proximable function. Our numerical experiments demonstrate that the proposed ADMM-based approach for PARAFAC2 can accurately recover the underlying components from simulated data while being both computationally efficient and flexible in terms of imposing constraints.
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