Abstract

We describe a new algorithm, termed subspace evolution and transfer (SET), for solving consistent low-rank matrix completion problems. The algorithm takes as its input a subset of entries of a low-rank matrix and outputs one low-rank matrix consistent with the given observations. The completion task is accomplished by searching for a column space in the Grassmann manifold that matches the incomplete observations. The SET algorithm consists of two parts-subspace evolution and subspace transfer. In the evolution part, we use a gradient descent method on the Grassmann manifold to refine our estimate of the column space. Since the gradient descent algorithm is not guaranteed to converge due to the existence of barriers along the search path, we design a new mechanism for detecting barriers and transferring the estimated column space across the barriers. This mechanism constitutes the core of the transfer step of the algorithm. The SET algorithm exhibits excellent empirical performance for a large range of sampling rates.

Original languageEnglish (US)
Article number5753950
Pages (from-to)3120-3132
Number of pages13
JournalIEEE Transactions on Signal Processing
Volume59
Issue number7
DOIs
StatePublished - Jul 1 2011

Keywords

  • Grassmann manifold
  • linear subspace
  • matrix completion
  • non-convex optimization

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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