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 1052-6234Full text not available from this repository.
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.
|Uncontrolled Keywords:||Matrix completion Multivariate linear regression Predictorcorrector on quotient manifold Regularization path Riemannian optimization Trace norm Trust region|
|Divisions:||Div F > Control|
|Depositing User:||Cron job|
|Date Deposited:||16 Jul 2015 13:04|
|Last Modified:||25 Nov 2015 10:23|