The Mathematical Institute, University of Oxford, Eprints Archive

Low rank matrix completion by alternating steepest descent methods

Tanner, Jared and Wei, Ke (2014) Low rank matrix completion by alternating steepest descent methods. Technical Report. unspecified. (Submitted)

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Abstract

Matrix completion involves recovering a matrix from a subset of its entries by utilizing interdependency between the entries, typically through low rank structure. Despite the combinatorial nature of matrix completion, there are many computationally efficient algorithms which are effective for a broad class of matrices. In this paper, we introduce an alternating steepest descent algorithm (ASD) and a scaled variant, ScaledASD, for the fixed-rank matrix completion problem. Empirial evaluation of ASD and ScaledASD on both image in painting and random problems show they are competitive with other state-of-the-art matrix completion algorithms in terms of recoverable rank and overall computational time. In particular, their low per iteration computational complexity makes ASD and ScaledASD efficient for large size problems, especially when computing the solutions to moderate accuracy. A preliminary convergence analysis is also presented.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1838
Deposited By: Helen Taylor
Deposited On:13 May 2014 08:47
Last Modified:29 May 2015 19:32

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