A Note on Alternating Minimization Algorithm for the Matrix Completion Problem

Journal Article · 06 June 2016 · IEEE Signal Processing Letters

DOI: https://doi.org/10.1109/LSP.2016.2576979 · OSTI ID:1361478

Gamarnik, David ^[1]; Misra, Sidhant  ^[2]

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1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Here, we consider the problem of reconstructing a low-rank matrix from a subset of its entries and analyze two variants of the so-called alternating minimization algorithm, which has been proposed in the past.We establish that when the underlying matrix has rank one, has positive bounded entries, and the graph underlying the revealed entries has diameter which is logarithmic in the size of the matrix, both algorithms succeed in reconstructing the matrix approximately in polynomial time starting from an arbitrary initialization.We further provide simulation results which suggest that the second variant which is based on the message passing type updates performs significantly better.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE Laboratory Directed Research and Development (LDRD) Program; National Science Foundation of China
• Grant/Contract Number: AC52-06NA25396; CMMI-1335155
• OSTI ID: 1361478
• Report Number(s): LA-UR-16-23854; TRN: US1702183
• Journal Information: IEEE Signal Processing Letters, Vol. 23, Issue 10; ISSN 1070-9908
• Publisher: IEEE Signal Processing SocietyCopyright Statement
• Country of Publication: United States
• Language: English