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Joint Approximate Diagonalization Method

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Abstract

The joint approximate diagonalization (JAD) method is a means to find an orthogonal matrix U according to the least squares or weighted least squares criteria to diagonalize a data matrix, which can be a covariance matrix or cumulant matrix. Since the 1990s, as the solution of the statistical identification problem, JAD has been used to extract information from the feature structure of the data matrix. For example, the forth-order joint cumulant matrix presented by Cardoso[1], the cumulant matrix generalized by Moreau[2] is greater or equal to the third-order cumulant matrix, SOBI (Second-Order Blind Identification) algorithm developed by Belouchrani, [3, 4] and second derivative matrix of the logarithmic characteristic matrix[5], etc. The major advantage of the JAD method is its high efficiency, Jacobi-like technology alternative least square, parallel factor analysis, and subspace fitting, etc. For infinite samples, JAD can calculate the common feature structure from any part of matrix set A or linear combination of matrix in A ; but for finite samples T, the matrices in set A T can’t accurately share the same feature structure. The viewpoint of statistics, an “averaging” processing should be used to improve accuracy and robustness, then an appropriate weighting can obtain a mean structure. Details will be discussed in Section 5 of this chapter.

Keywords

Blind Source Separation Mixed Signal Transfer Function Matrix Blind Separation Nonparametric Density Estimation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Shanghai Jiao Tong University Press, Shanghai and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Institute of Vibration Shock & NoiseShanghai Jiao Tong UniversityShanghaiChina

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