### 抄録

The applications of Non-Negative Tensor Factorization (NNTF) is an important tool for brain wave (EEG) analysis. For it to work efficiently, it is essential for NNTF to have a unique solution. In this paper we give a sufficient condition for NNTF to have a unique global optimal solution. For a third-order tensor T we define a matrix by some rearrangement of T and it is shown that the rank of the matrix is less than or equal to the rank of T. It is also shown that if both ranks are equal to r, the decomposition into a sum of r tensors of rank 1 is unique under some assumption.

元の言語 | 英語 |
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ホスト出版物のタイトル | Independent Component Analysis and Signal Separation - 7th International Conference, ICA 2007, Proceedings |

ページ | 113-120 |

ページ数 | 8 |

巻 | 4666 LNCS |

出版物ステータス | 出版済み - 2007 |

イベント | 7th International Conference on Independent Component Analysis (ICA) and Source Separation, ICA 2007 - London, 英国 継続期間: 9 9 2007 → 9 12 2007 |

### 出版物シリーズ

名前 | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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巻 | 4666 LNCS |

ISSN（印刷物） | 03029743 |

ISSN（電子版） | 16113349 |

### その他

その他 | 7th International Conference on Independent Component Analysis (ICA) and Source Separation, ICA 2007 |
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国 | 英国 |

市 | London |

期間 | 9/9/07 → 9/12/07 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science

### これを引用

*Independent Component Analysis and Signal Separation - 7th International Conference, ICA 2007, Proceedings*(巻 4666 LNCS, pp. 113-120). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); 巻数 4666 LNCS).

**A sufficient condition for the unique solution of non-negative tensor factorization.** / Sumi, Toshio; Sakata, Toshio.

研究成果: 著書/レポートタイプへの貢献 › 会議での発言

*Independent Component Analysis and Signal Separation - 7th International Conference, ICA 2007, Proceedings.*巻. 4666 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 巻. 4666 LNCS, pp. 113-120, 7th International Conference on Independent Component Analysis (ICA) and Source Separation, ICA 2007, London, 英国, 9/9/07.

}

TY - GEN

T1 - A sufficient condition for the unique solution of non-negative tensor factorization

AU - Sumi, Toshio

AU - Sakata, Toshio

PY - 2007

Y1 - 2007

N2 - The applications of Non-Negative Tensor Factorization (NNTF) is an important tool for brain wave (EEG) analysis. For it to work efficiently, it is essential for NNTF to have a unique solution. In this paper we give a sufficient condition for NNTF to have a unique global optimal solution. For a third-order tensor T we define a matrix by some rearrangement of T and it is shown that the rank of the matrix is less than or equal to the rank of T. It is also shown that if both ranks are equal to r, the decomposition into a sum of r tensors of rank 1 is unique under some assumption.

AB - The applications of Non-Negative Tensor Factorization (NNTF) is an important tool for brain wave (EEG) analysis. For it to work efficiently, it is essential for NNTF to have a unique solution. In this paper we give a sufficient condition for NNTF to have a unique global optimal solution. For a third-order tensor T we define a matrix by some rearrangement of T and it is shown that the rank of the matrix is less than or equal to the rank of T. It is also shown that if both ranks are equal to r, the decomposition into a sum of r tensors of rank 1 is unique under some assumption.

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UR - http://www.scopus.com/inward/citedby.url?scp=38149027181&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:38149027181

SN - 9783540744931

VL - 4666 LNCS

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

SP - 113

EP - 120

BT - Independent Component Analysis and Signal Separation - 7th International Conference, ICA 2007, Proceedings

ER -