In the particular case e7737c9ed7edde190c7645e4a21d2ec" title="Click to view the MathML source">R=K, the new bound above is equivalent to the bound e7be3a942149e8bcf315" title="Click to view the MathML source">R≤(I−1)(J−1) which is known to be necessary and sufficient for the generic uniqueness of the CPD. An existing algebraic algorithm (based on simultaneous diagonalization of a set of matrices) computes the CPD under the more restrictive constraint b8e7eb69ba9e9b03" title="Click to view the MathML source">R(R−1)≤I(I−1)J(J−1)/2 (implying that ). We give an example of a low-dimensional but high-rank CPD that cannot be found by optimization-based algorithms in a reasonable amount of time while our approach takes less than a second. We demonstrate that, at least for e433221b8d83af6f" title="Click to view the MathML source">R≤24, our algorithm can recover the rank-1 tensors in the CPD up to e7be3a942149e8bcf315" title="Click to view the MathML source">R≤(I−1)(J−1).
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