Some theory on Non-negative Tucker Decomposition

Abstract : 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 non-negative 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.
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Jérémy E. Cohen, Pierre Comon, Nicolas Gillis. Some theory on Non-negative Tucker Decomposition. 13th International Conference on Latent Variable Analysis and Signal Separation (LVA/ICA 2017), Feb 2017, Grenoble, France. ⟨hal-01420297⟩

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