### 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 | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 655-662 |

Number of pages | 8 |

Volume | 7063 LNCS |

Edition | PART 2 |

DOIs | |

Publication status | Published - 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) |
---|---|

Number | PART 2 |

Volume | 7063 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(PART 2 ed., Vol. 7063 LNCS, 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

**A modified multiplicative update algorithm for euclidean distance-based nonnegative matrix factorization and its global convergence.** / Hibi, Ryota; Takahashi, Norikazu.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*PART 2 edn, vol. 7063 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 2, vol. 7063 LNCS, pp. 655-662, 18th International Conference on Neural Information Processing, ICONIP 2011, Shanghai, China, 11/13/11. https://doi.org/10.1007/978-3-642-24958-7_76

}

TY - GEN

T1 - A modified multiplicative update algorithm for euclidean distance-based nonnegative matrix factorization and its global convergence

AU - Hibi, Ryota

AU - Takahashi, Norikazu

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

KW - Euclidean distance

KW - global convergence

KW - multiplicative update

KW - nonnegative matrix factorization

UR - http://www.scopus.com/inward/record.url?scp=81855227209&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=81855227209&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-24958-7_76

DO - 10.1007/978-3-642-24958-7_76

M3 - Conference contribution

AN - SCOPUS:81855227209

SN - 9783642249570

VL - 7063 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 655

EP - 662

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -