Exact Matrix Completion via Convex Optimization

We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen? We show that one can perfectly recover most low-rank matrices from what appears to be an incomplete set of entries. We prove that if the number m of sampled entries obeys

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Emmanuel J. Candès, Benjamin Recht
• Keywords: CORR 2008, Data Matrix, Education, Matrix, Matrix M