Orthonormal approximate joint block-diagonalization

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Authors C. Févotte & F. Theis
Journal/Conference Name GET/Télécom Paris
Paper Category
Paper Abstract The aim of this work is to give a comprehensive overview of the problem of jointly block-diagonalizing a set of matrices. We discuss how to implement methods in the common case of only approximative blockdiagonalizability using Jacobi algorithms. Standard Jacobi optimization techniques for diagonalization and joint diagonalization are reviewed first, before we study their generalizations to the block case and give some new theoretical insights on existence and uniqueness issues as well as on the interplay between block and standard diagonalization problems. Simulations on synthetic data show that in the block case convergence to the optimal solution is not always observed in practice and that the behavior of the Jacobi approach is very much dependent on the initialization of the orthonormal basis and also on the choice of the successive rotations.
Date of publication 2007
Code Programming Language MATLAB
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