Coupled matrix and tensor factorizations (CMTF) are frequently used to jointly analyze data from multiple sources, also called data fusion. However, different characteristics of datasets stemming from multiple sources pose many challenges in data fusion and require to employ various regularizations, constraints, loss functions and different types of coupling structures between datasets. In this paper, we propose a flexible algorithmic framework for coupled matrix and tensor factorizations which utilizes Alternating Optimization (AO) and the Alternating Direction Method of Multipliers (ADMM). The framework facilitates the use of a variety of constraints, loss functions and couplings with linear transformations in a seamless way. Numerical experiments on simulated and real datasets demonstrate that the proposed approach is accurate, and computationally efficient with comparable or better performance than available CMTF methods for Frobenius norm loss, while being more flexible. Using Kullback-Leibler divergence on count data, we demonstrate that the algorithm yields accurate results also for other loss functions.

中文翻译：

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具有线性耦合的正则化矩阵张量分解的灵活优化框架

耦合矩阵和张量分解 (CMTF) 经常用于联合分析来自多个来源的数据，也称为数据融合。然而，来自多个来源的数据集的不同特征给数据融合带来了许多挑战，需要在数据集之间采用各种正则化、约束、损失函数和不同类型的耦合结构。在本文中，我们为耦合矩阵和张量分解提出了一种灵活的算法框架，该框架利用交替优化 (AO) 和乘法器交替方向法 (ADMM)。该框架有助于以无缝方式使用各种约束、损失函数和线性变换耦合。在模拟和真实数据集上的数值实验表明，所提出的方法是准确的，计算效率与可用的 CMTF 方法相比，具有与 Frobenius 范数损失相当或更好的性能，同时更灵活。在计数数据上使用 Kullback-Leibler 散度，我们证明该算法也为其他损失函数产生准确的结果。