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. © Springer-Verlag Berlin Heidelberg 2007.
CITATION STYLE
Sumi, T., & Sakata, T. (2007). A sufficient condition for the unique solution of non-negative tensor factorization. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4666 LNCS, pp. 113–120). Springer Verlag. https://doi.org/10.1007/978-3-540-74494-8_15
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