[Comp-neuro] simultaneous matrix diagonalization

Klaus Obermayer oby at cs.tu-berlin.de
Fri Jun 30 11:41:27 CEST 2006


Dear All,

I would like to announce the implementation of the QDIAG algorithm for
simultaneous matrix diagonalization (e.g. for source separation
problems).

The software is available for downloading via the web-address:

http://ni.cs.tu-berlin.de/software/

using the link "QDIAG".

The QDIAG-method is described in detail in the upcoming publication:

R. Vollgraf and K. Obermayer, Quadratic Optimization for Simultaneous
Matrix Diagonalization, IEEE Transaction on Signal Processing, 2006,
in press.

The abstract is attached.

All the best

Klaus

------------------------------------------------------------------------

Quadratic Optimization for Simultaneous Matrix Diagonalization

R. Vollgraf and K. Obermayer

Simultaneous diagonalization of a set of matrices is a technique, which
has numerous applications in statistical signal processing and
multi-variate statistics. Although objective functions in a least
squares sense can be easily formulated, their minimization is not 
trivial, because constraints and 4th order terms are usually involved.
Most known optimization algorithms are, therefore, subject to certain
restrictions on the class of problems: orthogonal transformations, sets
of symmetric, hermitian or positive definite matrices, to name a few. In
this work we present a new algorithm called QDIAG, that splits the
overall optimization problem into a sequence of simpler second order
sub-problems. There are no restrictions imposed on the transformation
matrix, which may be non-orthogonal, indefnite or even rectangular, and
there are no restrictions, except for one, imposed on the matrices to
be diagonalized, regarding their symmetry or definiteness. We apply the
new method to Second Order Blind Source Separation and show that the
algorithm convergences fast and reliably. It allows for an
implementation with a complexity independent of the number of matrices
and, therefore, is particularly suitable for problems dealing with
large sets of matrices.

------------------------------------------------------------------------

Prof. Dr. Klaus Obermayer         phone:  49-30-314-73442
FR2-1, NI, Fakultaet IV                   49-30-314-73120
Technische Universitaet Berlin    fax:    49-30-314-73121
Franklinstrasse 28/29             e-mail: oby at cs.tu-berlin.de
10587 Berlin, Germany             http://ni.cs.tu-berlin.de/



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