### Abstract

The low-rank matrix completion problem can be stated as follows: given a subset of the entries of a matrix, find a low-rank matrix consistent with the observations. There exist several low-complexity algorithms for low-rank matrix completion which focus on the minimization of the Frobenius norm of the matrix projection residue. This optimization framework has inherent difficulties: the objective function is not continuous and the solution set is not closed. To address this problem, we propose a geometric objective function to replace the Frobenius norm: the new objective function is continuous everywhere and the solution set is the closure of the solution set of the Frobenius metric. Furthermore, using the geometric objective function and a simple gradient descent procedure, we are able to preclude the existence of local minimizers, and hence establish strong performance guarantees for special completion scenarios, which do not require matrix incoherence or large matrix size.

Original language | English (US) |
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Title of host publication | 2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings |

Pages | 3740-3743 |

Number of pages | 4 |

DOIs | |

State | Published - Aug 18 2011 |

Event | 36th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Prague, Czech Republic Duration: May 22 2011 → May 27 2011 |

### Publication series

Name | ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings |
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ISSN (Print) | 1520-6149 |

### Other

Other | 36th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 |
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Country | Czech Republic |

City | Prague |

Period | 5/22/11 → 5/27/11 |

### Keywords

- geometry
- low rank
- matrix completion

### ASJC Scopus subject areas

- Software
- Signal Processing
- Electrical and Electronic Engineering

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## Cite this

*2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings*(pp. 3740-3743). [5947164] (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). https://doi.org/10.1109/ICASSP.2011.5947164