### Abstract

Hierarchical alternating least squares (HALS) algorithms are efficient computational methods for nonnegative matrix factorization (NMF). Given an initial solution, HALS algorithms update the solution block by block iteratively so that the error decreases monotonically. However, update rules in HALS algorithms are not well-defined. In addition, due to this problem, the convergence of the sequence of solutions to a stationary point cannot be proved theoretically. In this paper, we consider the HALS algorithm for the Frobenius norm-based NMF, and prove that a modified version has the global convergence property in the sense of Zangwill.

Original language | English |
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Title of host publication | 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 21-24 |

Number of pages | 4 |

ISBN (Print) | 9781479919635 |

DOIs | |

Publication status | Published - Jan 14 2016 |

Event | 6th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015 - Cancun, Mexico Duration: Dec 13 2015 → Dec 16 2015 |

### Other

Other | 6th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015 |
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Country | Mexico |

City | Cancun |

Period | 12/13/15 → 12/16/15 |

### Fingerprint

### ASJC Scopus subject areas

- Signal Processing
- Computational Mathematics

### Cite this

*2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015*(pp. 21-24). [7383726] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CAMSAP.2015.7383726

**Global convergence of a modified HALS algorithm for nonnegative matrix factorization.** / Kimura, Takumi; Takahashi, Norikazu.

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

*2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015.*, 7383726, Institute of Electrical and Electronics Engineers Inc., pp. 21-24, 6th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015, Cancun, Mexico, 12/13/15. https://doi.org/10.1109/CAMSAP.2015.7383726

}

TY - GEN

T1 - Global convergence of a modified HALS algorithm for nonnegative matrix factorization

AU - Kimura, Takumi

AU - Takahashi, Norikazu

PY - 2016/1/14

Y1 - 2016/1/14

N2 - Hierarchical alternating least squares (HALS) algorithms are efficient computational methods for nonnegative matrix factorization (NMF). Given an initial solution, HALS algorithms update the solution block by block iteratively so that the error decreases monotonically. However, update rules in HALS algorithms are not well-defined. In addition, due to this problem, the convergence of the sequence of solutions to a stationary point cannot be proved theoretically. In this paper, we consider the HALS algorithm for the Frobenius norm-based NMF, and prove that a modified version has the global convergence property in the sense of Zangwill.

AB - Hierarchical alternating least squares (HALS) algorithms are efficient computational methods for nonnegative matrix factorization (NMF). Given an initial solution, HALS algorithms update the solution block by block iteratively so that the error decreases monotonically. However, update rules in HALS algorithms are not well-defined. In addition, due to this problem, the convergence of the sequence of solutions to a stationary point cannot be proved theoretically. In this paper, we consider the HALS algorithm for the Frobenius norm-based NMF, and prove that a modified version has the global convergence property in the sense of Zangwill.

UR - http://www.scopus.com/inward/record.url?scp=84963930473&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84963930473&partnerID=8YFLogxK

U2 - 10.1109/CAMSAP.2015.7383726

DO - 10.1109/CAMSAP.2015.7383726

M3 - Conference contribution

SN - 9781479919635

SP - 21

EP - 24

BT - 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015

PB - Institute of Electrical and Electronics Engineers Inc.

ER -