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Detecting the rank of a symmetric tensor

Abstract : This paper deals with the problem of CanonicalPolyadic (CP) decomposition of a given tensor. Standard al-gorithms to perform this decomposition generally require theknowledge of the rank of the sought tensor decomposition. Yet,determining the rank of a given tensor is generally hard. In thispaper, we propose a method to find the rank of a symmetrictensor. We reformulate the CP decomposition problem into atruncated moment problem and we derive a sufficient conditionto certify the rank of the tensor from the rank of some momentmatrices associated with it. For tensors with rank not exceedinga prescribed value, this sufficient condition is also necessary.Finally, we propose to combine our rank detection procedurewith existing algorithms. Experimental results show the validityof our results and provide an illustration of its practical use.Our method provides the correct rank even in the presence amoderate level of noise.
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https://hal.archives-ouvertes.fr/hal-02284991
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Submitted on : Thursday, September 12, 2019 - 1:35:47 PM
Last modification on : Wednesday, August 5, 2020 - 3:43:55 AM
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Arthur Marmin, Marc Castella, Jean-Christophe Pesquet. Detecting the rank of a symmetric tensor. EUSIPCO 2019 : 27th European Signal Processing Conference, Sep 2019, La Corogne, Spain. pp.1-5, ⟨10.23919/EUSIPCO.2019.8902781⟩. ⟨hal-02284991⟩

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