Jacobi Angles for Simultaneous Diagonalization
SIAM Journal on Matrix Analysis and Applications
Blind source separation via the second characteristic function
Signal Processing
Self-Organising Neural Networks: Independent Component Analysis and Blind Source Separation
Self-Organising Neural Networks: Independent Component Analysis and Blind Source Separation
Joint Approximate Diagonalization of Positive Definite Hermitian Matrices
SIAM Journal on Matrix Analysis and Applications
Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications
Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications
The Journal of Machine Learning Research
A blind source separation technique using second-order statistics
IEEE Transactions on Signal Processing
Comments on blind beamforming for multiple non-Gaussian signals andthe constant-modulus algorithm
IEEE Transactions on Signal Processing
Algebraic Joint Zero-Diagonalization and Blind Sources Separation
IEEE Transactions on Signal Processing
Blind Identification of Underdetermined Mixtures by Simultaneous Matrix Diagonalization
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Nonorthogonal Joint Diagonalization Free of Degenerate Solution
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
On blind beamforming for multiple non-Gaussian signals and theconstant-modulus algorithm
IEEE Transactions on Signal Processing
Nonorthogonal Joint Diagonalization Algorithm Based on Trigonometric Parameterization
IEEE Transactions on Signal Processing
Frequency domain blind MIMO system identification based on second and higher order statistics
IEEE Transactions on Signal Processing
Quadratic optimization for simultaneous matrix diagonalization
IEEE Transactions on Signal Processing
A generalization of joint-diagonalization criteria for sourceseparation
IEEE Transactions on Signal Processing
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To make the results reasonable, existing joint diagonalization algorithms have imposed a variety of constraints on diagonalizers. Actually, those constraints can be imposed uniformly by minimizing the condition number of diagonalizers. Motivated by this, the approximate joint diagonalization problem is reviewed as a multiobjective optimization problem for the first time. Based on this, a new algorithm for nonorthogonal joint diagonalization is developed. The new algorithm yields diagonalizers which not only minimize the diagonalization error but also have as small condition numbers as possible. Meanwhile, degenerate solutions are avoided strictly. Besides, the new algorithm imposes few restrictions on the target set of matrices to be diagonalized, which makes it widely applicable. Primary results on convergence are presented and we also show that, for exactly jointly diagonalizable sets, no local minima exist and the solutions are unique under mild conditions. Extensive numerical simulations illustrate the performance of the algorithm and provide comparison with other leading diagonalization methods. The practical use of our algorithm is shown for blind source separation (BSS) problems, especially when ill-conditioned mixing matrices are involved.