The Geometry of Algorithms with Orthogonality Constraints
SIAM Journal on Matrix Analysis and Applications
The Expected Norm of Random Matrices
Combinatorics, Probability and Computing
Fast monte-carlo algorithms for finding low-rank approximations
Journal of the ACM (JACM)
Fast computation of low-rank matrix approximations
Journal of the ACM (JACM)
Restricted Boltzmann machines for collaborative filtering
Proceedings of the 24th international conference on Machine learning
Optimization Algorithms on Matrix Manifolds
Optimization Algorithms on Matrix Manifolds
The power of convex relaxation: near-optimal matrix completion
IEEE Transactions on Information Theory
Matrix completion from a few entries
IEEE Transactions on Information Theory
ADMiRA: atomic decomposition for minimum rank approximation
IEEE Transactions on Information Theory
Distributed rating prediction in user generated content streams
Proceedings of the fifth ACM conference on Recommender systems
Item popularity and recommendation accuracy
Proceedings of the fifth ACM conference on Recommender systems
Recovering Low-Rank and Sparse Components of Matrices from Incomplete and Noisy Observations
SIAM Journal on Optimization
Identifying users from their rating patterns
Proceedings of the 2nd Challenge on Context-Aware Movie Recommendation
Exact matrix completion via convex optimization
Communications of the ACM
Online learning in the embedded manifold of low-rank matrices
The Journal of Machine Learning Research
Transfer learning to predict missing ratings via heterogeneous user feedbacks
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Three
Circle-based recommendation in online social networks
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Low-rank Matrix Recovery via Iteratively Reweighted Least Squares Minimization
SIAM Journal on Optimization
Restricted strong convexity and weighted matrix completion: optimal bounds with noise
The Journal of Machine Learning Research
On top-k recommendation using social networks
Proceedings of the sixth ACM conference on Recommender systems
A fast tri-factorization method for low-rank matrix recovery and completion
Pattern Recognition
Transfer learning in heterogeneous collaborative filtering domains
Artificial Intelligence
Sparkler: supporting large-scale matrix factorization
Proceedings of the 16th International Conference on Extending Database Technology
Evaluation of recommendations: rating-prediction and ranking
Proceedings of the 7th ACM conference on Recommender systems
Robust localization from incomplete local information
IEEE/ACM Transactions on Networking (TON)
A survey of collaborative filtering based social recommender systems
Computer Communications
| Hi-index | 0.02 |
Given a matrix M of low-rank, we consider the problem of reconstructing it from noisy observations of a small, random subset of its entries. The problem arises in a variety of applications, from collaborative filtering (the 'Netflix problem') to structure-from-motion and positioning. We study a low complexity algorithm introduced by Keshavan, Montanari, and Oh (2010), based on a combination of spectral techniques and manifold optimization, that we call here OPTSPACE. We prove performance guarantees that are order-optimal in a number of circumstances.