CUED Publications database

Low-rank optimization with trace norm penalty

Mishra, B and Meyer, G and Bach, F and Sepulchre, R (2013) Low-rank optimization with trace norm penalty. SIAM Journal on Optimization, 23. pp. 2124-2149. ISSN 1052-6234

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Abstract

The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization that makes the trace norm differentiable in the search space and the computation of duality gap numerically tractable. The search space is nonlinear but is equipped with a Riemannian structure that leads to efficient computations. We present a second-order trust-region algorithm with a guaranteed quadratic rate of convergence. Overall, the proposed optimization scheme converges superlinearly to the global solution while maintaining complexity that is linear in the number of rows and columns of the matrix. To compute a set of solutions efficiently for a grid of regularization parameters we propose a predictor-corrector approach that outperforms the naive warm-restart approach on the fixed-rank quotient manifold. The performance of the proposed algorithm is illustrated on problems of low-rank matrix completion and multivariate linear regression. © 2013 Society for Industrial and Applied Mathematics.

Item Type: Article
Uncontrolled Keywords: Matrix completion Multivariate linear regression Predictorcorrector on quotient manifold Regularization path Riemannian optimization Trace norm Trust region
Subjects: UNSPECIFIED
Divisions: Div F > Control
Depositing User: Cron Job
Date Deposited: 07 Mar 2014 11:27
Last Modified: 08 Dec 2014 02:10
DOI: 10.1137/110859646