Low-rank optimization with trace norm penalty - Inria - Institut national de recherche en sciences et technologies du numérique
Journal Articles SIAM Journal on Optimization Year : 2013

Low-rank optimization with trace norm penalty

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 particular 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 super-linearly 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.
Fichier principal
Vignette du fichier
lowrank_mishra_siopt.pdf (762.78 Ko) Télécharger le fichier
Origin Publisher files allowed on an open archive
Loading...

Dates and versions

hal-00924110 , version 1 (06-01-2014)

Identifiers

Cite

Bamdev Mishra, Gilles Meyer, Francis Bach, Rodolphe Sepulchre. Low-rank optimization with trace norm penalty. SIAM Journal on Optimization, 2013, 23 (4), pp.2124-2149. ⟨10.1137/110859646⟩. ⟨hal-00924110⟩
403 View
209 Download

Altmetric

Share

More