Abstract
A class of simple Jacobi-type algorithms for non-orthogonal matrix joint diagonalization based on the LU or QR factorization is introduced. By appropriate parametrization of the underlying manifolds, i.e. using triangular and orthogonal Jacobi matrices we replace a high dimensional minimization problem by a sequence of simple one dimensional minimization problems. In addition, a new scale-invariant cost function for non-orthogonal joint diagonalization is employed. These algorithms are step-size free. Numerical simulations demonstrate the efficiency of the methods.
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Afsari, B., Krishnaprasad, P.S.: A Novel Non-orthogonal Joint Diagonalization Cost Function for ICA, ISR technical report (2005), Available at, http://techreports.isr.umd.edu/reports/2005/TR_2005-106.pdf
Afsari, B.: Gradient Flow Based Matrix Joint Diagonalization for Independent Componenet Analysis, MS Thesis, ECE Department, University of Maryland, College Park (May 2004), Available at, http://techreports.isr.umd.edu/reports/2004/MS_2004-4.pdf
Afsari, B., Krishnaprasad, P.S.: Some Gradient Based Joint Diagonalization Methods for ICA. In: Puntonet, C.G., Prieto, A.G. (eds.) ICA 2004. LNCS, vol. 3195, pp. 437–444. Springer, Heidelberg (2004)
Cardoso, J.F., Soulumiac, A.: Blind Beamforming For Non-Gauusian Signals. IEE Proceedings 140(6) (December 1993)
Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. Johns Hopkins University Press (1996)
Pham, D.T., Cardoso, J.F.: Blind separation of instantaneous mixtures of non stationary sources. IEEE Trans. Signal Processing 49(9), 1837–1848 (2001)
Yeredor, A.: Non-Orthogonal Joint Diagonalization in the Least-Squares Sense With Application in Blind Source Separation. IEEE Transactions on Signal Processing 50(7) (July 2002)
Ziehe, A., Kawanabe, M., Harmeling, S., Mller, K.-R.: A Fast Algorithm for Joint Diagonalization with Non-orthogonal Transformations and its Application to Blind Source Separation. Journal of Machine Learning Research 5, 801–818 (2004)
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Afsari, B. (2006). Simple LU and QR Based Non-orthogonal Matrix Joint Diagonalization. In: Rosca, J., Erdogmus, D., Príncipe, J.C., Haykin, S. (eds) Independent Component Analysis and Blind Signal Separation. ICA 2006. Lecture Notes in Computer Science, vol 3889. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11679363_1
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DOI: https://doi.org/10.1007/11679363_1
Publisher Name: Springer, Berlin, Heidelberg
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