Genericity and Rank Deficiency of High Order Symmetric Tensors
Pierre Comon, Bernard Mourrain, Lek-Heng Lim and Gene Golub
In: ICASSP2006, May 14-19, 2006, Toulouse, France.
Blind Identification of Under-Determined Mixtures (UDM) is involved
in numerous applications, including Multi-Way factor Analysis (MWA)
and Signal Processing. In the latter case, the use of High-Order
Statistics (HOS) like Cumulants leads to the decomposition of
symmetric tensors. Yet, little has been published about
rank-revealing decompositions of symmetric tensors. Definitions of
rank are discussed, and useful results on Generic Rank are proved,
with the help of tools borrowed from Algebraic Geometry.