Numerical methods for simultaneous diagonalization
SIAM Journal on Matrix Analysis and Applications
Jacobi Angles for Simultaneous Diagonalization
SIAM Journal on Matrix Analysis and Applications
Matrix computations (3rd ed.)
Joint Approximate Diagonalization of Positive Definite Hermitian Matrices
SIAM Journal on Matrix Analysis and Applications
The Journal of Machine Learning Research
Simple LU and QR based non-orthogonal matrix joint diagonalization
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
A blind source separation technique using second-order statistics
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Nonorthogonal Joint Diagonalization Algorithm Based on Trigonometric Parameterization
IEEE Transactions on Signal Processing
Quadratic optimization for simultaneous matrix diagonalization
IEEE Transactions on Signal Processing
QML-based joint diagonalization of positive-definite hermitian matrices
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Joint eigenvalue decomposition using polar matrix factorization
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
Complex non-orthogonal joint diagonalization based on LU and LQ decompositions
LVA/ICA'12 Proceedings of the 10th international conference on Latent Variable Analysis and Signal Separation
A parallel dual matrix method for blind signal separation
Neural Computation
| Hi-index | 35.69 |
A new algorithm for computing the nonorthogonal joint diagonalization of a set of matrices is proposed for independent component analysis and blind source separation applications. This algorithm is an extension of the Jacobi-like algorithm first proposed in the joint approximate diagonalization of eigenmatrices (JADE) method for orthogonaljoirit diagonalization. The improvement consists mainly in computing a mixing matrix of determinant one and columns of equal norm instead of an orthogonal mixing matrix. This target matrix is constructed iteratively by successive multiplications of not only Givens rotations but also hyperbolic rotations and diagonal matrices. The algorithm performance, evaluated on synthetic data, compares favorably with existing methods in terms of speed of convergence and complexity.