Identifiability of an X-Rank Decomposition of Polynomial Maps

Pierre Comon, Yang Qi, Konstantin Usevich

Abstract: In this paper, we study a polynomial decomposition model that arises in problems of system identification, signal processing, and machine learning. We show that this decomposition is a special case of the X-rank decomposition---a powerful novel concept in algebraic geometry that generalizes the tensor CP decomposition. We prove new results on generic/maximal rank and on identifiability of a particular polynomial decomposition model. We try to make the results and basic tools accessible to a general audience (i.e., assuming no knowledge of algebraic geometry or its prerequisites).