Structured low-rank matrix learning

A Unified Framework for Structured Low-rank Matrix Learning

Authors

P. Jawanpuria and B. Mishra

Abstract

We propose a novel optimization approach for learning a low-rank matrix which is also constrained to lie in a linear subspace. Exploiting a particular variational characterization of the squared trace norm regularizer, we formulate the structured low-rank matrix learning problem as a rank-constrained saddle point minimax problem. The proposed modeling decouples the low- rank and structural constraints onto separate factors. The optimization problem is formulated on the Riemannian spectrahedron manifold, where the Riemannian framework allows to propose computationally efficient conjugate gradient and trust-region algorithms. Our approach easily accommodates popular non-smooth loss functions, e.g., l1-loss, and our algorithms are scalable to large-scale problem instances. The numerical comparisons show that our proposed algorithms outperform state-of-the-art algorithms in standard and robust matrix completion, stochastic realization, and multi-task feature learning problems on various benchmarks.

Downloads

• Status: ICML, 2018.
• Paper: [Publisher’s pdf][arXiv:1704.07352][Presentation].
• Matlab code: Structured_matrix_learning_18Feb2018.zip. Inductive matrix completion code with side information is available at Inductive_matrix_completion_28Apr2018.zip.
  • 28 Apr 2018: inductive matrix completion code included.
  • 18 Feb 2018: added non-negative matrix completion code.
  • 19 May 2017: added a better optimized code for matrix completion.
  • 06 May 2017: added robust matrix completion code.
  • 27 April 2017: code is online. It contains matrix completion and Hankel matrix learning implementations.

Examples