Low-rank Matrix Completion with Noisy Observations: a Quantitative Comparison
Provides a practical comparison of matrix completion algorithms for practitioners in collaborative filtering, computer vision, and sensor networks.
The paper compares three matrix completion algorithms (OptSpace, ADMiRA, FPCA) on noisy observations, showing they can accurately reconstruct both real and synthetic matrices.
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.