Low-rank Matrix Completion with Noisy Observations: a Quantitative Comparison

Abstract

We consider a problem of significant practical importance, namely, the reconstruction of a low-rank data matrix from a small subset of its entries. This problem appears in many areas such as collaborative filtering, computer vision and wireless sensor networks. In this paper, we focus on the matrix completion problem in the case when the observed samples are corrupted by noise. We compare the performance of three state-of-the-art matrix completion algorithms (OptSpace, ADMiRA and FPCA) on a single simulation platform and present numerical results. We show that in practice these efficient algorithms can be used to reconstruct real data matrices, as well as randomly generated matrices, accurately.

7 pages, 7 figures, 47th Allerton Conference on Communication Control and Computing, 2009, invited paper

References in corpus (8)

• Matrix Completion from a Few Entries
• Guaranteed Rank Minimization via Singular Value Projection
• Matrix Completion With Noise
• Exact Matrix Completion via Convex Optimization
• Fixed Point and Bregman Iterative Methods for Matrix Rank Minimization
• The Power of Convex Relaxation: Near-Optimal Matrix Completion
• ADMiRA: Atomic Decomposition for Minimum Rank Approximation
• SET: an algorithm for consistent matrix completion

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