Matrix Completion with Cross-Concentrated Sampling: Bridging Uniform Sampling and CUR Sampling

Abstract

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.

References in corpus (6)

• Hierarchical structure and the prediction of missing links in networks
• Matrix Completion on Graphs
• CUR Algorithm for Partially Observed Matrices
• Structured Gradient Descent for Fast Robust Low-Rank Hankel Matrix Completion
• Mode-wise Tensor Decompositions: Multi-dimensional Generalizations of CUR Decompositions
• Riemannian CUR Decompositions for Robust Principal Component Analysis

Cited by in corpus (6)

• On the Robustness of Cross-Concentrated Sampling for Matrix Completion
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• Subset Random Sampling and Reconstruction of Finite Time-Vertex Graph Signals
• Non-convex approaches for low-rank tensor completion under tubal sampling
• Structured Sampling for Robust Euclidean Distance Geometry
• Randomized Approach to Matrix Completion: Applications in Recommendation Systems and Image Inpainting