Identifiability of an X-rank decomposition of polynomial maps
  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. In the paper, we try to make results and basic tools accessible for general audience (assuming no knowledge of algebraic geometry or its prerequisites). 
Pierre Comon, Yang Qi, Konstantin Usevich
cs.IT math.IT math.NA stat.ML