### Abstract

We propose a novel iterative algorithm for nonnegative matrix factorization with the alpha-divergence. The proposed algorithm is based on the coordinate descent and the Newton method. We show that the proposed algorithm has the global convergence property in the sense that the sequence of solutions has at least one convergent subsequence and the limit of any convergent subsequence is a stationary point of the corresponding optimization problem. We also show through numerical experiments that the proposed algorithm is much faster than the multiplicative update rule.

Original language | English |
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Title of host publication | Neural Information Processing - 24th International Conference, ICONIP 2017, Proceedings |

Publisher | Springer Verlag |

Pages | 335-344 |

Number of pages | 10 |

Volume | 10634 LNCS |

ISBN (Print) | 9783319700861 |

DOIs | |

Publication status | Published - Jan 1 2017 |

Event | 24th International Conference on Neural Information Processing, ICONIP 2017 - Guangzhou, China Duration: Nov 14 2017 → Nov 18 2017 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10634 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 24th International Conference on Neural Information Processing, ICONIP 2017 |
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Country | China |

City | Guangzhou |

Period | 11/14/17 → 11/18/17 |

### Fingerprint

### Keywords

- Alpha-divergence
- Global convergence
- Newton method
- Nonnegative matrix factorization

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Neural Information Processing - 24th International Conference, ICONIP 2017, Proceedings*(Vol. 10634 LNCS, pp. 335-344). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10634 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-70087-8_36

**A novel newton-type algorithm for nonnegative matrix factorization with alpha-divergence.** / Nakatsu, Satoshi; Takahashi, Norikazu.

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

*Neural Information Processing - 24th International Conference, ICONIP 2017, Proceedings.*vol. 10634 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10634 LNCS, Springer Verlag, pp. 335-344, 24th International Conference on Neural Information Processing, ICONIP 2017, Guangzhou, China, 11/14/17. https://doi.org/10.1007/978-3-319-70087-8_36

}

TY - GEN

T1 - A novel newton-type algorithm for nonnegative matrix factorization with alpha-divergence

AU - Nakatsu, Satoshi

AU - Takahashi, Norikazu

PY - 2017/1/1

Y1 - 2017/1/1

N2 - We propose a novel iterative algorithm for nonnegative matrix factorization with the alpha-divergence. The proposed algorithm is based on the coordinate descent and the Newton method. We show that the proposed algorithm has the global convergence property in the sense that the sequence of solutions has at least one convergent subsequence and the limit of any convergent subsequence is a stationary point of the corresponding optimization problem. We also show through numerical experiments that the proposed algorithm is much faster than the multiplicative update rule.

AB - We propose a novel iterative algorithm for nonnegative matrix factorization with the alpha-divergence. The proposed algorithm is based on the coordinate descent and the Newton method. We show that the proposed algorithm has the global convergence property in the sense that the sequence of solutions has at least one convergent subsequence and the limit of any convergent subsequence is a stationary point of the corresponding optimization problem. We also show through numerical experiments that the proposed algorithm is much faster than the multiplicative update rule.

KW - Alpha-divergence

KW - Global convergence

KW - Newton method

KW - Nonnegative matrix factorization

UR - http://www.scopus.com/inward/record.url?scp=85035081672&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85035081672&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-70087-8_36

DO - 10.1007/978-3-319-70087-8_36

M3 - Conference contribution

SN - 9783319700861

VL - 10634 LNCS

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

SP - 335

EP - 344

BT - Neural Information Processing - 24th International Conference, ICONIP 2017, Proceedings

PB - Springer Verlag

ER -