Shahid Beheshti UniversityComputational Mathematics and Computer Modeling with Applications (CMCMA)2783-48591120220601On rank decomposition and semi-symmetric rank decomposition of semi-symmetric tensors374710199310.52547/CMCMA.1.1.37ENHassanBozorgmaneshDepartment of Applied Mathematics, Faculty of Mathematical Sciences,
Shahid Beheshti University, Tehran, IranAnthony TheodoreChronopoulosDepartment of Computer Science, University of Texas, San Antonio, Texas
78249, USA.
(Visiting Faculty) Department of Computer Engineering & Informatics, University of
Patras, Rio 26500, Greece.Journal Article20211124A tensor is called semi-symmetric if all modes but one, are symmetric. In this paper, we study the CP decomposition of semi-symmetric tensors or higher-order individual difference scaling (INDSCAL). Comon's conjecture states that for any symmetric tensor, the CP rank and symmetric CP rank are equal, while it is known that Comon's conjecture is not true in the general case but it is proved under several assumptions in the literature. In the paper, Comon's conjecture is extended for semi-symmetric CP decomposition and CP decomposition of semi-symmetric tensors under suitable assumptions. Specially, we show that if a semi-symmetric tensor has a CP rank smaller or equal to its order, or when the semi-symmetric CP rank is less than/or equal to the dimension, then the semi-symmetric CP rank is equal to the CP rank.https://cmcma.sbu.ac.ir/article_101993_3d209bbe504397a58dee9c25066bf2da.pdf