Graph-Regularized Non-Negative Tensor-Ring Decomposition for Multiway Representation Learning
Graph-Regularized Non-Negative Tensor-Ring Decomposition for Multiway Representation Learning
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DOI：
10.1109/tcyb.2022.3157133
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发表时间：
2022-04
影响因子：
11.8
通讯作者：
Yuyuan Yu;Guoxu Zhou;Ning Zheng;Yuning Qiu;Shengli Xie;Qibin Zhao
中科院分区：
文献类型：
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作者：
Yuyuan Yu;Guoxu Zhou;Ning Zheng;Yuning Qiu;Shengli Xie;Qibin Zhao
张量环分解是利用多路数据低秩性的有力工具，在许多重要应用中显示出巨大的潜力。本文提出了非负TR(NTR)分解和图正则NTR(GNTR)分解。前者通过对核心张量施加非负性来学习基于零件的表示，而后者则在NTR模型中引入了图形正则化，以从张量数据中获取流形几何信息。这两种模型都是对树分解的扩展，可以作为非负多路数据表示学习的有力工具。针对NTR和GNTR，推导了基于加速近邻梯度的优化算法。我们还从经验上证明了所提出的方法可以提供更可解释和更有物理意义的表示。例如，它们能够从对象中提取具有有意义的颜色和线条图案的基于零件的零部件。大量的实验结果表明，该方法在聚类和分类任务中的性能优于现有的基于张量的方法。
Tensor-ring (TR) decomposition is a powerful tool for exploiting the low-rank property of multiway data and has been demonstrated great potential in a variety of important applications. In this article, non-negative TR (NTR) decomposition and graph-regularized NTR (GNTR) decomposition are proposed. The former equips TR decomposition with the ability to learn the parts-based representation by imposing non-negativity on the core tensors, and the latter additionally introduces a graph regularization to the NTR model to capture manifold geometry information from tensor data. Both of the proposed models extend TR decomposition and can be served as powerful representation learning tools for non-negative multiway data. The optimization algorithms based on an accelerated proximal gradient are derived for NTR and GNTR. We also empirically justified that the proposed methods can provide more interpretable and physically meaningful representations. For example, they are able to extract parts-based components with meaningful color and line patterns from objects. Extensive experimental results demonstrated that the proposed methods have better performance than state-of-the-art tensor-based methods in clustering and classification tasks.