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

Toshio Sumi, Toshio Sakata

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish
Title of host publicationIndependent Component Analysis and Signal Separation - 7th International Conference, ICA 2007, Proceedings
Pages113-120
Number of pages8
Publication statusPublished - Dec 1 2007
Event7th International Conference on Independent Component Analysis (ICA) and Source Separation, ICA 2007 - London, United Kingdom
Duration: Sep 9 2007Sep 12 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4666 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other7th International Conference on Independent Component Analysis (ICA) and Source Separation, ICA 2007
CountryUnited Kingdom
CityLondon
Period9/9/079/12/07

Fingerprint

Brain Waves
Factorization
Unique Solution
Tensors
Electroencephalography
Tensor
Non-negative
Sufficient Conditions
Less than or equal to
Rearrangement
Brain
Optimal Solution
Decomposition
Decompose

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Sumi, T., & Sakata, T. (2007). A sufficient condition for the unique solution of non-negative tensor factorization. In 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.

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Sumi, T & Sakata, T 2007, A sufficient condition for the unique solution of non-negative tensor factorization. in 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.
Sumi T, Sakata T. A sufficient condition for the unique solution of non-negative tensor factorization. In Independent Component Analysis and Signal Separation - 7th International Conference, ICA 2007, Proceedings. 2007. p. 113-120. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Sumi, Toshio ; Sakata, Toshio. / A sufficient condition for the unique solution of non-negative tensor factorization. Independent Component Analysis and Signal Separation - 7th International Conference, ICA 2007, Proceedings. 2007. pp. 113-120 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{3e76302e1e0a41f9babb8c355028020d,
title = "A sufficient condition for the unique solution of non-negative tensor factorization",
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.",
author = "Toshio Sumi and Toshio Sakata",
year = "2007",
month = "12",
day = "1",
language = "English",
isbn = "9783540744931",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "113--120",
booktitle = "Independent Component Analysis and Signal Separation - 7th International Conference, ICA 2007, Proceedings",

}

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.

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

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

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 -