Some theoretical difficulties that arise from dimensionality reduction for tensors with non-negative coefficients is discussed in this paper. A necessary and sufficient condition is derived for a low nonnegative rank tensor to admit a non-negative Tucker decomposition with a core of the same non-negative rank. Moreover, we provide evidence that the only algorithm operating mode-wise, minimizing the dimensions of the features spaces, and that can guarantee the non-negative core to have low non-negative rank requires identifying on each mode a cone with possibly a very large number of extreme rays. To illustrate our observations, some existing algorithms that compute the non-negative Tucker decomposition are described and tested on synthetic data.
CITATION STYLE
Cohen, J. E., Comon, P., & Gillis, N. (2017). Some theory on non-negative tucker decomposition. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10169 LNCS, pp. 152–161). Springer Verlag. https://doi.org/10.1007/978-3-319-53547-0_15
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