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

Toshio Sumi; Toshio Sakata

doi:10.1007/978-3-540-74494-8_15

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

Toshio Sumi, Toshio Sakata

Division for Theoretical Natural Science

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English
Title of host publication	Independent Component Analysis and Signal Separation - 7th International Conference, ICA 2007, Proceedings
Publisher	Springer Verlag
Pages	113-120
Number of pages	8
ISBN (Print)	9783540744931
DOIs	https://doi.org/10.1007/978-3-540-74494-8_15
Publication status	Published - 2007
Event	7th International Conference on Independent Component Analysis (ICA) and Source Separation, ICA 2007 - London, United Kingdom Duration: Sept 9 2007 → Sept 12 2007

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
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
Country/Territory	United Kingdom
City	London
Period	9/9/07 → 9/12/07

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-540-74494-8_15

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). Springer Verlag. https://doi.org/10.1007/978-3-540-74494-8_15

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. Springer Verlag, 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 proceeding › Conference 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, Springer Verlag, pp. 113-120, 7th International Conference on Independent Component Analysis (ICA) and Source Separation, ICA 2007, London, United Kingdom, 9/9/07. https://doi.org/10.1007/978-3-540-74494-8_15

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. Springer Verlag. 2007. p. 113-120. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-74494-8_15

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. Springer Verlag, 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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A sufficient condition for the unique solution of non-negative tensor factorization

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