Weighted Matrix Completion and Recovery With Prior Subspace Information | IEEE Journals & Magazine | IEEE Xplore

Weighted Matrix Completion and Recovery With Prior Subspace Information


Abstract:

An incoherent low-rank matrix can be efficiently reconstructed after observing a few of its entries at random, and then, solving a convex program that minimizes the nucle...Show More

Abstract:

An incoherent low-rank matrix can be efficiently reconstructed after observing a few of its entries at random, and then, solving a convex program that minimizes the nuclear norm. In many applications, in addition to these entries, potentially valuable prior knowledge about the column and row spaces of the matrix is also available to the practitioner. In this paper, we incorporate this prior knowledge in matrix completion-by minimizing a weighted nuclear norm-and precisely quantify any improvements. In particular, we find in theory that reliable prior knowledge reduces the sample complexity of matrix completion by a logarithmic factor, and the observed improvement in numerical simulations is considerably more magnified. We also present similar results for the closely related problem of matrix recovery from generic linear measurements.
Published in: IEEE Transactions on Information Theory ( Volume: 64, Issue: 6, June 2018)
Page(s): 4044 - 4071
Date of Publication: 16 March 2018

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