Error-controlling algorithm for simultaneous block-diagonalization and its application to independent component analysis. (English) Zbl 1271.65080

Maehara, Takanori; Murota, Kazuo

JSIAM Lett. 2, 131-134 (2010).

Summary: The finest simultaneous block-diagonalization for a given set of square matrices has been studied independently in the area of independent component analysis (ICA) and semidefinite programming. A new algorithm for this problem, which finds the finest decomposition with a capability of coping with numerical errors, has recently been proposed by the present authors. In this paper, we indicate the use of the algorithm for ICA by describing its main features and comparing the method with the other existing methods.

MSC:

65F30	Other matrix algorithms (MSC2010)
62H25	Factor analysis and principal components; correspondence analysis
90C22	Semidefinite programming
65F15	Numerical computation of eigenvalues and eigenvectors of matrices

Keywords:

simultaneous block-diagonalization; independent component analysis; eigenvalue problem; numerical examples; independent component analysis; semidefinite programming; algorithm