TY - JOUR
ID - 101993
TI - On rank decomposition and semi-symmetric rank decomposition of semi-symmetric tensors
JO - Computational Mathematics and Computer Modeling with Applications (CMCMA)
JA - CMCMA
LA - en
SN -
AU - Bozorgmanesh, Hassan
AU - Chronopoulos, Anthony Theodore
AD - Department of Applied Mathematics, Faculty of Mathematical Sciences,
Shahid Beheshti University, Tehran, Iran
AD - Department of Computer Science, University of Texas, San Antonio, Texas
78249, USA.
(Visiting Faculty) Department of Computer Engineering & Informatics, University of
Patras, Rio 26500, Greece.
Y1 - 2022
PY - 2022
VL - 1
IS - 1
SP - 37
EP - 47
KW - INDSCAL
KW - semi-symmetric tensor
KW - CP decomposition
KW - CP rank
KW - semi-symmetric decomposition
DO - 10.52547/CMCMA.1.1.37
N2 - A 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.
UR - https://cmcma.sbu.ac.ir/article_101993.html
L1 - https://cmcma.sbu.ac.ir/article_101993_3d209bbe504397a58dee9c25066bf2da.pdf
ER -