On the second eigenvalue of random regular graphs
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
The Geometry of Algorithms with Orthogonality Constraints
SIAM Journal on Matrix Analysis and Applications
Spectral techniques applied to sparse random graphs
Random Structures & Algorithms
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Accurate low-rank matrix recovery from a small number of linear measurements
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
The power of convex relaxation: near-optimal matrix completion
IEEE Transactions on Information Theory
Spatiotemporal imaging with partially separable functions: a matrix recovery approach
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
ADMiRA: atomic decomposition for minimum rank approximation
IEEE Transactions on Information Theory
Proceedings of the 6th International COnference
Uniqueness of Low-Rank Matrix Completion by Rigidity Theory
SIAM Journal on Matrix Analysis and Applications
Transactional Database Transformation and Its Application in Prioritizing Human Disease Genes
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Short paper: location privacy: user behavior in the field
Proceedings of the second ACM workshop on Security and privacy in smartphones and mobile devices
On traffic matrix completion in the internet
Proceedings of the 2012 ACM conference on Internet measurement conference
DMFSGD: a decentralized matrix factorization algorithm for network distance prediction
IEEE/ACM Transactions on Networking (TON)
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Let M be an nα × n matrix of rank r ≪ n, and assume that a uniformly random subset E of its entries is observed. We describe an efficient algorithm that reconstructs M from |E| = O(r n) observed entries with relative root mean square error RMSE ≤ C(α) (nr/|E|)1/2. Further, if r = O(1) and M is sufficiently unstructured, then it can be reconstructed exactly from |E| = O(n log n) entries. This settles (in the case of bounded rank) a question left open by Candès and Recht and improves over the guarantees for their reconstruction algorithm. The complexity of our algorithm is O(|E|r log n), which opens the way to its use for massive data sets. In the process of proving these statements, we obtain a generalization of a celebrated result by Friedman-Kahn-Szemerédi and Feige-Ofek on the spectrum of sparse random matrices.