Paper Info
Title
RTRMC: A Riemannian trust-region method for low-rank matrix completion.
Abstract
We consider large matrices of low rank. We address the problem of recovering such matrices when most of the entries are unknown. Matrix completion finds applications in recommender systems. In this setting, the rows of the matrix may correspond to items and the columns may correspond to users. The known entries are the ratings given by users to some items. The aim is to predict the unobserved ratings. This problem is commonly stated in a constrained optimization framework. We follow an approach that exploits the geometry of the low-rank constraint to recast the problem as an unconstrained optimization problem on the Grassmann manifold. We then apply first- and second-order Riemannian trust-region methods to solve it. The cost of each iteration is linear in the number of known entries. Our methods, RTRMC 1 and 2, outperform state-of-the-art algorithms on a wide range of problem instances.
Year
Venue
Field
2011
NIPS
Recommender system,Trust region,Mathematical optimization,Matrix completion,Matrix (mathematics),Computer science,Low-rank approximation,Artificial intelligence,Grassmannian,Optimization problem,Machine learning,Constrained optimization
DocType
Citations 
PageRank 
Conference
11
0.67
References 
Authors
7
2
Name
Order
Citations
PageRank
Boumal, Nicolas117814.50
Pierre-Antoine Absil234834.17