DocumentCode :
699985
Title :
Gradient based Approximate Joint Diagonalization by orthogonal transforms
Author :
Sorensen, Mikael ; Icart, Sylvie ; Comon, Pierre ; Deneire, Luc
Author_Institution :
Lab. I3S, UNSA, Sophia Antipolis, France
fYear :
2008
fDate :
25-29 Aug. 2008
Firstpage :
1
Lastpage :
5
Abstract :
Approximate Joint Diagonalization (AJD) of a set of symmetric matrices by an orthogonal transform is a popular problem in Blind Source Separation (BSS). In this paper we propose a gradient based algorithm which maximizes the sum of squares of diagonal entries of all the transformed symmetric matrices. Our main contribution is to transform the orthogonality constrained optimization problem into an unconstrained problem. This transform is performed in two steps: First by parameterizing the orthogonal transform matrix by the matrix exponential of a skew-symmetric matrix. Second, by introducing an isomorphism between the vector space of skew-symmetric matrices and the Euclidean vector space of appropriate dimension. This transform is then applied to a gradient based algorithm called GAEX to perform joint diagonalization of a set of symmetric matrices.
Keywords :
approximation theory; blind source separation; gradient methods; optimisation; Euclidean vector space; GAEX; approximate joint diagonalization; blind source separation; gradient based algorithm; gradient based approximate joint diagonalization; isomorphism; orthogonal transform matrix; orthogonality constrained optimization problem; skew-symmetric matrices; skew-symmetric matrix; symmetric matrices; Europe; Joints; Signal processing; Signal processing algorithms; Symmetric matrices; Transforms; Vectors;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Signal Processing Conference, 2008 16th European
Conference_Location :
Lausanne
ISSN :
2219-5491
Type :
conf
Filename :
7080517
Link To Document :
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