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

Toshio Sumi, Toshio Sakata

研究成果: 著書/レポートタイプへの貢献会議での発言

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
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
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 20079 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)
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
英国
London
期間9/9/079/12/07

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

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

これを引用

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

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

研究成果: 著書/レポートタイプへの貢献会議での発言

Sumi, T & Sakata, T 2007, A sufficient condition for the unique solution of non-negative tensor factorization. : 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.
Sumi T, Sakata T. A sufficient condition for the unique solution of non-negative tensor factorization. : Independent Component Analysis and Signal Separation - 7th International Conference, ICA 2007, Proceedings. 巻 4666 LNCS. 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. 巻 4666 LNCS 2007. pp. 113-120 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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