论文标题
朱莉娅：张量完成的联合多线性和非线性识别
JULIA: Joint Multi-linear and Nonlinear Identification for Tensor Completion
论文作者
论文摘要
张量的完成旨在将部分观察到的张量归纳缺失条目。现有的张量完成方法通常假设潜在组件之间的多线性或非线性关系。 但是，现实世界中的张力具有更复杂的模式，在这些模式中，多线性和非线性关系都可以共存。在这种情况下，现有方法不足以描述数据结构。本文提出了一个联合多线性和非线性识别（Julia）框架，以完成大规模张量的完成。朱莉娅（Julia）统一了具有多个优点的多线性和非线性张量完成模型，而不是现有方法：1）灵活模型选择，即，它通过将其值分配为多线性和非线性组件的组合来拟合张量； 2）与现有的非线性张量完成方法兼容； 3）基于精心设计的交替优化方法的有效培训。对六个真正的大规模张量的实验表明，朱莉娅的表现优于许多现有的张量完成算法。此外，朱莉娅可以提高一类非线性张量完成方法的性能。结果表明，在一些大规模的张量完成方案中，使用朱莉娅的基线方法能够获得均值均值较低的55％降低55％，并节省了67％的计算复杂性。
Tensor completion aims at imputing missing entries from a partially observed tensor. Existing tensor completion methods often assume either multi-linear or nonlinear relationships between latent components. However, real-world tensors have much more complex patterns where both multi-linear and nonlinear relationships may coexist. In such cases, the existing methods are insufficient to describe the data structure. This paper proposes a Joint mUlti-linear and nonLinear IdentificAtion (JULIA) framework for large-scale tensor completion. JULIA unifies the multi-linear and nonlinear tensor completion models with several advantages over the existing methods: 1) Flexible model selection, i.e., it fits a tensor by assigning its values as a combination of multi-linear and nonlinear components; 2) Compatible with existing nonlinear tensor completion methods; 3) Efficient training based on a well-designed alternating optimization approach. Experiments on six real large-scale tensors demonstrate that JULIA outperforms many existing tensor completion algorithms. Furthermore, JULIA can improve the performance of a class of nonlinear tensor completion methods. The results show that in some large-scale tensor completion scenarios, baseline methods with JULIA are able to obtain up to 55% lower root mean-squared-error and save 67% computational complexity.
