On almost sure identifiability of non multilinear tensor decomposition

Uniqueness of tensor decompositions is of crucial importance in numerous engineering applications. Extensive work in algebraic geometry has given various bounds involving tensor rank and dimensions to ensure generic identifiability. However, most of this work is hardly accessible to non-specialists, and does not apply to non-multilinear models. In this paper, we present another approach, using the Jacobian of the model. The latter sheds a new light on bounds and exceptions previously obtained. Finally, the method proposed is applied to a non-multilinear decomposition used in fluorescence spectrometry, which permits to state generic local identifiability.