Title :
Least Squares Approximate Joint Diagonalization on the Orthogonal Group
Author :
Tanaka, T. ; Fiori, Simone
Author_Institution :
Dept. of Electr. & Electron. Eng., Tokyo Univ. of Agric. & Technol., Japan
Abstract :
The theory and derivation of a novel method for approximate joint diagonalization (AJD) on the orthogonal group of matrices are presented. The proposed algorithms are fast and simple, hence, easy to implement. We introduce a least-squares-type cost function, which is to be minimized under the constraint that the matrix to be sought for is orthogonal. A gradient flow for optimizing such cost function is derived and its stability is analyzed within the framework of differential geometry. It is proposed to numerically approximate the gradient flow by using a geodesic-based and an Euler-like update algorithms. Numerical examples about blind source separation of speech signals are illustrated to support the analysis.
Keywords :
blind source separation; differential geometry; least squares approximations; matrix algebra; speech processing; Euler-like update algorithms; blind source separation; cost function; differential geometry; geodesic-based algorithms; gradient flow; least squares approximate joint diagonalization; least-squares-type cost function; orthogonal group; speech signals; Agriculture; Blind source separation; Cost function; Geometry; Least squares approximation; Signal analysis; Source separation; Speech analysis; Stability analysis; Symmetric matrices; Adaptive learning; blind source separation; gradient flow; joint diagonalization; orthogonal group;
Conference_Titel :
Acoustics, Speech and Signal Processing, 2007. ICASSP 2007. IEEE International Conference on
Conference_Location :
Honolulu, HI
Print_ISBN :
1-4244-0727-3
DOI :
10.1109/ICASSP.2007.366319
