### Abstract

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.

Original language | English |
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Title of host publication | Independent Component Analysis and Signal Separation - 7th International Conference, ICA 2007, Proceedings |

Pages | 113-120 |

Number of pages | 8 |

Publication status | Published - Dec 1 2007 |

Event | 7th International Conference on Independent Component Analysis (ICA) and Source Separation, ICA 2007 - London, United Kingdom Duration: Sep 9 2007 → Sep 12 2007 |

### 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 | 4666 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 7th International Conference on Independent Component Analysis (ICA) and Source Separation, ICA 2007 |
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Country | United Kingdom |

City | London |

Period | 9/9/07 → 9/12/07 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

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

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

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

*Independent Component Analysis and Signal Separation - 7th International Conference, ICA 2007, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4666 LNCS, pp. 113-120, 7th International Conference on Independent Component Analysis (ICA) and Source Separation, ICA 2007, London, United Kingdom, 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 - 2007/12/1

Y1 - 2007/12/1

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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M3 - Conference contribution

AN - SCOPUS:38149027181

SN - 9783540744931

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 -