Nonlinear dynamical control systems
Nonlinear dynamical control systems
Geometric optimization methods for adaptive filtering
Geometric optimization methods for adaptive filtering
Independent component analysis, a new concept?
Signal Processing - Special issue on higher order statistics
Adaptive filter theory (3rd ed.)
Adaptive filter theory (3rd ed.)
Matrix computations (3rd ed.)
Natural gradient works efficiently in learning
Neural Computation
Differential and Numerically Invariant Signature Curves Applied to Object Recognition
International Journal of Computer Vision
Independent component analysis: theory and applications
Independent component analysis: theory and applications
Nonlinear Control Systems
Projective residual vector quantization and mapped residual pooling
ICASSP '00 Proceedings of the Acoustics, Speech, and Signal Processing, 2000. on IEEE International Conference - Volume 04
Code-length-based universal extraction for blind signal separation
ICASSP '00 Proceedings of the Acoustics, Speech, and Signal Processing, 2000. on IEEE International Conference - Volume 06
Adaptive paraunitary filter banks for contrast-based multichannel blind deconvolution
ICASSP '01 Proceedings of the Acoustics, Speech, and Signal Processing, 2001. on IEEE International Conference - Volume 05
An adaptive blind signal separation based on the joint optimization of Givens rotations
ICASSP '01 Proceedings of the Acoustics, Speech, and Signal Processing, 2001. on IEEE International Conference - Volume 05
Blind separation of instantaneous mixture of sources via anindependent component analysis
IEEE Transactions on Signal Processing
Equivariant adaptive source separation
IEEE Transactions on Signal Processing
Manifold studies of nonlinear antenna array geometries
IEEE Transactions on Signal Processing
Statistical dynamics of on-line independent component analysis
The Journal of Machine Learning Research
Statistical dynamics of on-line independent component analysis
The Journal of Machine Learning Research
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A primary purpose of this paper is to provide a focused tutorial on basic concepts in differential geometry in order to explain the rationale for "natural gradient" adaptation algorithms. A vectorized notation is employed to provide a new derivation of the natural gradient as a pullback. Based on this foundation, contravariant adaptation on structured matrices, such as Bezout, Toeplitz, orthogonal, or Vandermonde, is presented. A target application, with simulations demonstrating results, is blind source separation.