论文标题
在度量学习约束下用于张量恢复的双杆优化方法
A Bilevel Optimization Method for Tensor Recovery Under Metric Learning Constraints
论文作者
论文摘要
张量完成和张量分解是许多域中的重要问题。在这项工作中，我们利用这些问题之间的联系来学习一个距离指标，以改善分解和完成。我们表明，完成任务的最佳Mahalanobis距离度量与已完成张量的Tucker分解密切相关。然后，我们制定一个双重优化问题，以执行受公制学习约束的关节张量完成和分解。公制学习限制还使我们能够灵活地将相似性侧信息和耦合矩阵（如果可用）融合到张量恢复过程中。我们得出了一种算法来解决二聚体优化问题并证明其全局收敛性。在对实际数据进行评估时，与以前的方法相比，我们的方法的性能明显更好。
Tensor completion and tensor decomposition are important problems in many domains. In this work, we leverage the connection between these problems to learn a distance metric that improves both decomposition and completion. We show that the optimal Mahalanobis distance metric for the completion task is closely related to the Tucker decomposition of the completed tensor. Then, we formulate a bilevel optimization problem to perform joint tensor completion and decomposition, subject to metric learning constraints. The metric learning constraints also allow us to flexibly incorporate similarity side information and coupled matrices, when available, into the tensor recovery process. We derive an algorithm to solve the bilevel optimization problem and prove its global convergence. When evaluated on real data, our approach performs significantly better compared to previous methods.
