Asymptotic Convergence Rate of Alternating Minimization for Rank One Matrix Completion

Rui Liu; Alex Olshevsky

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arXiv · 2008.04988

Asymptotic Convergence Rate of Alternating Minimization for Rank One Matrix Completion

Rui Liu·Alex Olshevsky

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Abstract

We study alternating minimization for matrix completion in the simplest possible setting: completing a rank-one matrix from a revealed subset of the entries. We bound the asymptotic convergence rate by the variational characterization of eigenvalues of a reversible consensus problem. This leads to a polynomial upper bound on the asymptotic rate in terms of number of nodes as well as the largest degree of the graph of revealed entries.

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Rui Liu, Alex Olshevsky. 2020-08-11. Asymptotic Convergence Rate of Alternating Minimization for Rank One Matrix Completion. https://arxiv.org/abs/2008.04988

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