### Abstract

Nonnegative matrix factorization (NMF) is to approximate a given large nonnegative matrix by the product of two small nonnegative matrices. Although the multiplicative update algorithm is widely used as an efficient computation method for NMF, it has a serious drawback that the update formulas are not well-defined because they are expressed in the form of a fraction. Furthermore, due to this drawback, the global convergence of the algorithm has not been guaranteed. In this paper, we consider NMF in which the approximation error is measured by the Euclidean distance between two matrices. We propose a modified multiplicative update algorithm in order to overcome the drawback of the original version and prove its global convergence.

Original language | English |
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Title of host publication | Neural Information Processing - 18th International Conference, ICONIP 2011, Proceedings |

Pages | 655-662 |

Number of pages | 8 |

Edition | PART 2 |

DOIs | |

Publication status | Published - Nov 28 2011 |

Externally published | Yes |

Event | 18th International Conference on Neural Information Processing, ICONIP 2011 - Shanghai, China Duration: Nov 13 2011 → Nov 17 2011 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Number | PART 2 |

Volume | 7063 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 18th International Conference on Neural Information Processing, ICONIP 2011 |
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Country | China |

City | Shanghai |

Period | 11/13/11 → 11/17/11 |

### Keywords

- Euclidean distance
- global convergence
- multiplicative update
- nonnegative matrix factorization

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Neural Information Processing - 18th International Conference, ICONIP 2011, Proceedings*(PART 2 ed., pp. 655-662). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7063 LNCS, No. PART 2). https://doi.org/10.1007/978-3-642-24958-7_76