Learning Algorithms in Complex-Valued Neural Networks using Wirtinger Calculus

This chapter contains sections titled: Introduction Derivatives in Wirtinger Calculus Complex Gradient Learning Algorithms for Feedforward CVNNs Learning Algorithms for Recurrent CVNNs Conclusion

[1]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[2]  Ronald J. Williams,et al.  Experimental Analysis of the Real-time Recurrent Learning Algorithm , 1989 .

[3]  Tohru Nitta,et al.  An Extension of the Back-Propagation Algorithm to Complex Numbers , 1997, Neural Networks.

[4]  James L. Massey,et al.  Proper complex random processes with applications to information theory , 1993, IEEE Trans. Inf. Theory.

[5]  Paul J. Werbos,et al.  Backpropagation Through Time: What It Does and How to Do It , 1990, Proc. IEEE.

[6]  Roberto Battiti,et al.  First- and Second-Order Methods for Learning: Between Steepest Descent and Newton's Method , 1992, Neural Computation.

[7]  Tülay Adali,et al.  Approximation by Fully Complex Multilayer Perceptrons , 2003, Neural Computation.

[8]  Louis L. Scharf,et al.  Second-order analysis of improper complex random vectors and processes , 2003, IEEE Trans. Signal Process..

[9]  N. Sundararajan,et al.  A fully complex-valued radial basis function network and its learning algorithm. , 2009 .

[10]  Sergios Theodoridis,et al.  Ieee Transactions on Signal Processing Extension of Wirtinger's Calculus to Reproducing Kernel Hilbert Spaces and the Complex Kernel Lms , 2022 .

[11]  Liang Li,et al.  Nonlinear adaptive prediction of nonstationary signals , 1995, IEEE Trans. Signal Process..

[12]  Robert F. H. Fischer,et al.  Precoding and Signal Shaping for Digital Transmission , 2002 .

[13]  S. L. Goh,et al.  An Augmented Extended Kalman Filter Algorithm for Complex-Valued Recurrent Neural Networks , 2007, Neural Computation.

[14]  W. Wirtinger.  Zur formalen Theorie der Funktionen von mehr komplexen Veränderlichen , 1927 .

[15]  Kazuyuki Aihara,et al.  Complex-valued prediction of wind profile using augmented complex statistics , 2009 .

[16]  Ronald J. Williams,et al.  A Learning Algorithm for Continually Running Fully Recurrent Neural Networks , 1989, Neural Computation.

[17]  Mohammad Bagher Menhaj,et al.  Training feedforward networks with the Marquardt algorithm , 1994, IEEE Trans. Neural Networks.

[18]  Hualiang Li,et al.  Algorithms for Complex ML ICA and Their Stability Analysis Using Wirtinger Calculus , 2010, IEEE Transactions on Signal Processing.

[19]  Kazuyuki Murase,et al.  Wirtinger Calculus Based Gradient Descent and Levenberg-Marquardt Learning Algorithms in Complex-Valued Neural Networks , 2011, ICONIP.

[20]  Lee A. Feldkamp,et al.  Neurocontrol of nonlinear dynamical systems with Kalman filter trained recurrent networks , 1994, IEEE Trans. Neural Networks.

[21]  A. Bos.  Complex gradient and Hessian , 1994 .

[22]  Martin T. Hagan,et al.  Backpropagation Algorithms for a Broad Class of Dynamic Networks , 2007, IEEE Transactions on Neural Networks.

[23]  Francesco Piazza,et al.  On the complex backpropagation algorithm , 1992, IEEE Trans. Signal Process..

[24]  Hualiang Li,et al.  Complex-Valued Adaptive Signal Processing Using Nonlinear Functions , 2008, EURASIP J. Adv. Signal Process..

[25]  Danilo P. Mandic,et al.  A Complex-Valued RTRL Algorithm for Recurrent Neural Networks , 2004, Neural Computation.

[26]  Elias S. Manolakos,et al.  Training fully recurrent neural networks with complex weights , 1994 .

[27]  Danilo P. Mandic,et al.  Recurrent Neural Networks for Prediction , 2001 .