Path-connectedness of tensor ranks

Yang Qi (1) , Pierre Comon (2) , Lek-Heng Lim (1) , Ke Ye (3)

1 University of Chicago
2 GIPSA-CICS - GIPSA - Communication Information and Complex Systems
3 CAS - Chinese Academy of Sciences [Beijing]

Computations of low-rank approximations of tensors often involve path-following optimization algorithms. In such cases, a correct solution may only be found if there exists a continuous path connecting the initial point to a desired solution. We will investigate the existence of such a path in sets of low-rank tensors for various notions of ranks, including tensor rank, border rank, multilinear rank, and their counterparts for symmetric tensors.

Mots clés: symmetric multilinear rank; path-connectedness; Tensor Decomposition; symmetric rank; border rank; multilinear rank

Domaines: Traitement du signal et de l'image [eess.SP]; Intelligence artificielle [cs.AI]; Géométrie algébrique [math.AG]; Optimisation et contrôle [math.OC]

Yang Qi, Pierre Comon, Lek-Heng Lim, Ke Ye. Path-connectedness of tensor ranks. EUSIPCO 2019 - 27th European Signal Processing Conference, Sep 2019, A Coruna, Spain. ⟨10.23919/EUSIPCO.2019.8903027⟩. ⟨hal-02121152⟩