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

Authors:
Toshio Sumi;Toshio Sakata
Affiliations:
Faculty of Design, Kyushu University, Japan;Faculty of Design, Kyushu University, Japan
Venue:
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
Year:
2007

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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.