Paper ID sheet UCL-INMA-2019.06

Title

Riemannian gradient descent methods for graph-regularized matrix completion

Authors

Shuyu Dong, P.-A. Absil, K. A. Gallivan

Abstract

Low-rank matrix completion is the problem of recovering the missing entries of a data matrix by using the assumption that the true matrix admits a good low-rank approximation. Much attention has been given recently to exploiting correlations between the column/row entities to improve the matrix completion quality. In this paper, we propose preconditioned gradient descent algorithms for solving the low-rank matrix completion problem with graph Laplacian-based regularizers. Experiments on synthetic data show that our approach achieves signifficant speedup compared to an existing method based on alternating minimization. Experimental results on real world data also show that our methods provide low-rank solutions of similar quality in comparable or less time than the state-of-the-art method.

Key words

Status

Accepted for publication in Linear Algebra and its Applications

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• Publisher's version: doi:10.1016/j.laa.2020.06.010
• Preprint
• Code (provided with no warranty, support, or any other form of responsibility)
  The link above gives access to the code that reproduces the results of the paper. For a more user-friendly version, see https://github.com/shuyu-d/grmc.