论文标题
线性耦合的正规矩阵量因子化的灵活优化框架
A Flexible Optimization Framework for Regularized Matrix-Tensor Factorizations with Linear Couplings
论文作者
论文摘要
耦合矩阵和张量因子化（CMTF）经常用于共同分析来自多个来源的数据，也称为数据融合。但是，来自多个来源的数据集的不同特征在数据融合中构成了许多挑战，并需要采用各种正规化，约束，损失功能以及数据集之间的不同类型的耦合结构。在本文中，我们提出了一种用于耦合矩阵和张量因子化的灵活算法框架，该框架利用交替优化（AO）和乘数的交替方向方法（ADMM）。该框架有助于以无缝的方式使用各种约束，损耗函数和耦合。对模拟和真实数据集进行的数值实验表明，所提出的方法是准确的，并且比可用的CMTF方法具有可比性或更好的性能在计算上有效，而FROBENIUS NORK损失则更加灵活。使用计数数据上使用Kullback-Leibler差异，我们证明该算法也为其他损失函数得出准确的结果。
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.
