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Quadratic Optimization for Simultaneous Matrix Diagonalization (QDIAG)

On this page you can find a MATLAB implementation of the QDIAG algorithm for simultaneous matrix diagonalization. The following two files you may download, use, redistribute, and/or modify under the terms of the GNU General Public License.

qdiag.m - Simultaneous matrix diagonalization routine
corrmat.m - Computation of time-lagged correlation matrices

How to use these files is described here.

If you use this software for publication, please cite:

Quadratic Optimization for Simultaneous Matrix Diagonalization
Citation key Vollgraf2006c
Author Vollgraf, R. and Obermayer, K.
Pages 3270 – 3278
Year 2006
Journal IEEE Trans. Signal Processing Applications
Volume 54
Number 9
Abstract 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 de nite 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, inde nite or even rectangular, and there are no restrictions, except for one, imposed on the matrices to be diagonalized, regarding their symmetry or de niteness. 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.
Bibtex Type of Publication Selected:sources
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