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

Toshio Sumi, Toshio Sakata

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

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.

本文言語英語
ホスト出版物のタイトルIndependent Component Analysis and Signal Separation - 7th International Conference, ICA 2007, Proceedings
出版社Springer Verlag
ページ113-120
ページ数8
ISBN(印刷版)9783540744931
DOI
出版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(印刷版)0302-9743
ISSN(電子版)1611-3349

その他

その他7th International Conference on Independent Component Analysis (ICA) and Source Separation, ICA 2007
Country英国
CityLondon
Period9/9/079/12/07

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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