论文标题
矩阵完成，具有交叉浓缩抽样：桥接均匀抽样和CUR采样
Matrix Completion with Cross-Concentrated Sampling: Bridging Uniform Sampling and CUR Sampling
论文作者
论文摘要
虽然在矩阵完成文献中已广泛研究了均匀的采样，但CUR采样近似于通过行样品和列样品近似矩阵。不幸的是，在现实世界应用中，这两种采样模型在各种情况下都缺乏灵活性。在这项工作中，我们提出了一种新颖且易于实现的采样策略，即跨浓缩采样（CCS）。通过桥接统一的采样和CUR采样，CCS提供了额外的灵活性，可以节省应用程序中的采样成本。此外，我们还为基于CCS的矩阵完成提供了足够的条件。此外，我们提出了针对拟议的CCS模型的高效非凸算法，称为迭代CUR完成（ICURC）。数值实验验证了CCS和ICURC对均匀采样及其基线算法的经验优势，以及在合成数据集上。
While uniform sampling has been widely studied in the matrix completion literature, CUR sampling approximates a low-rank matrix via row and column samples. Unfortunately, both sampling models lack flexibility for various circumstances in real-world applications. In this work, we propose a novel and easy-to-implement sampling strategy, coined Cross-Concentrated Sampling (CCS). By bridging uniform sampling and CUR sampling, CCS provides extra flexibility that can potentially save sampling costs in applications. In addition, we also provide a sufficient condition for CCS-based matrix completion. Moreover, we propose a highly efficient non-convex algorithm, termed Iterative CUR Completion (ICURC), for the proposed CCS model. Numerical experiments verify the empirical advantages of CCS and ICURC against uniform sampling and its baseline algorithms, on both synthetic and real-world datasets.
