论文标题
基于PARAFAC2的耦合矩阵和张量因子化
PARAFAC2-based Coupled Matrix and Tensor Factorizations
论文作者
论文摘要
耦合矩阵和张量因子化（CMTF）已成为一种有效的数据融合工具，可以以矩阵和高阶张量的形式共同分析数据集。 PARAFAC2模型已证明是CandeComp/Parafac（CP）张量模型的一种有希望的替代方法，因为它的灵活性和能力处理了不规则/破烂的张量。尽管最近研究了基于parafac2模型与矩阵/张量分解的融合模型，但它们在数据集之间的可能正规化和/或类型的耦合方面受到限制。在本文中，我们提出了一个算法框架，用于拟合基于PARAFAC2的CMTF模型，并使用交替优化（AO）和乘数的交替方向方法（AMPM）对所有模式和线性耦合施加各种约束。通过数值实验，我们证明了所提出的算法方法可以使用各种约束和线性耦合准确地恢复基础模式。
Coupled matrix and tensor factorizations (CMTF) have emerged as an effective data fusion tool to jointly analyze data sets in the form of matrices and higher-order tensors. The PARAFAC2 model has shown to be a promising alternative to the CANDECOMP/PARAFAC (CP) tensor model due to its flexibility and capability to handle irregular/ragged tensors. While fusion models based on a PARAFAC2 model coupled with matrix/tensor decompositions have been recently studied, they are limited in terms of possible regularizations and/or types of coupling between data sets. In this paper, we propose an algorithmic framework for fitting PARAFAC2-based CMTF models with the possibility of imposing various constraints on all modes and linear couplings, using Alternating Optimization (AO) and the Alternating Direction Method of Multipliers (ADMM). Through numerical experiments, we demonstrate that the proposed algorithmic approach accurately recovers the underlying patterns using various constraints and linear couplings.
