Genericity And Rank Deficiency Of High Order Symmetric Tensors

Author

Comon, P. ; Mourrain, B. ; Lim, L.-H. ; Golub, G.H.

Author_Institution

Lab. I3S, CNRS

Volume

3

fYear

2006

fDate

14-19 May 2006

Abstract

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

Keywords

computational geometry; higher order statistics; signal processing; tensors; algebraic geometry; blind identification; generic rank; high order symmetric tensors; high-order statistics; multiway factor analysis; rank deficiency; signal processing; symmetric tensors decomposition; under-determined mixtures; Array signal processing; Biomedical signal processing; Geometry; Polynomials; Signal analysis; Signal processing algorithms; Singular value decomposition; Speech analysis; Statistics; Tensile stress;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech and Signal Processing, 2006. ICASSP 2006 Proceedings. 2006 IEEE International Conference on

Conference_Location

Toulouse

ISSN

1520-6149

Print_ISBN

1-4244-0469-X

Type

conf

DOI

10.1109/ICASSP.2006.1660606

Filename

1660606