On identifiability of higher order block term tensor decompositions of rank Lr⊗ rank-1

Abstract

ABSTRACTThe characteristics of tensor decomposition in certain desirable forms are its uniqueness which appears to be essential in many applications. Extensive work under the framework of algebraic geometry has provided many fundamental results associated with tensor rank and dimension to ensure the generic identifiability. Different from most current approaches in the literature, in this paper, by using algebraic geometry theory, we study the rank and rank rank-1 block term tensor decomposition for higher order tensors. In particular, we establish the sufficient and necessary conditions for a general tensor to have finitely many block term decompositions, and sufficient conditions to guarantee a unique decomposition.