Identifiability of an X-rank decomposition of polynomial maps
This addresses a foundational problem in algebraic geometry with applications across multiple fields, but it appears incremental as it builds on the X-rank concept.
The paper tackles the identifiability of a polynomial decomposition model used in system identification, signal processing, and machine learning, showing it is a special case of the X-rank decomposition and proving new results on generic/maximal rank and identifiability.
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).