Convergence analysis of the augmented complex klms algorithm with pre-tuned dictionary

Complex kernel-based adaptive algorithms have been recently introduced for complex-valued nonlinear system identification. These algorithms are built upon the same framework as complex linear adaptive filtering techniques and Wirtinger's calculus in complex reproducing kernel Hilbert spaces. In this paper, we study the convergence behavior of the augmented complex Gaussian KLMS algorithm. Simulation results illustrate the accuracy of the analysis.

[1]  Danilo P. Mandic,et al.  The quaternion kernel least squares , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[2]  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 .

[3]  Cédric Richard.  Filtrage adaptatif non-linéaire par méthodes de gradient stochastique court-terme à noyau , 2005 .

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

[5]  José Carlos Príncipe,et al.  Mixture kernel least mean square , 2013, The 2013 International Joint Conference on Neural Networks (IJCNN).

[6]  Ignacio Santamaría,et al.  A Sliding-Window Kernel RLS Algorithm and Its Application to Nonlinear Channel Identification , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[7]  Paul Honeine,et al.  Online Prediction of Time Series Data With Kernels , 2009, IEEE Transactions on Signal Processing.

[8]  Sergios Theodoridis,et al.  The Augmented Complex Kernel LMS , 2011, IEEE Transactions on Signal Processing.

[9]  Y. Engel.  Kernel Recursive Least Squares , 2004 .

[10]  Jie Chen,et al.  Kernel LMS algorithm with forward-backward splitting for dictionary learning , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[11]  Paul Honeine,et al.  On-line Nonlinear Sparse Approximation of Functions , 2007, 2007 IEEE International Symposium on Information Theory.

[12]  Sun-Yuan Kung,et al.  Kernel Approaches to Unsupervised and Supervised Machine Learning , 2009, PCM.

[13]  Weifeng Liu,et al.  The Kernel Least-Mean-Square Algorithm , 2008, IEEE Transactions on Signal Processing.

[14]  Don R. Hush,et al.  An Explicit Description of the Reproducing Kernel Hilbert Spaces of Gaussian RBF Kernels , 2006, IEEE Transactions on Information Theory.

[15]  Shie Mannor,et al.  The kernel recursive least-squares algorithm , 2004, IEEE Transactions on Signal Processing.

[16]  Cédric Richard,et al.  Closed-form conditions for convergence of the Gaussian kernel-least-mean-square algorithm , 2012, 2012 Conference Record of the Forty Sixth Asilomar Conference on Signals, Systems and Computers (ASILOMAR).

[17]  Masahiro Yukawa,et al.  Multikernel Adaptive Filtering , 2012, IEEE Transactions on Signal Processing.

[18]  Cédric Richard,et al.  Convex combinations of kernel adaptive filters , 2014, 2014 IEEE International Workshop on Machine Learning for Signal Processing (MLSP).

[19]  Cédric Richard,et al.  Stochastic Behavior Analysis of the Gaussian Kernel Least-Mean-Square Algorithm , 2012, IEEE Trans. Signal Process..

[20]  Danilo P. Mandic,et al.  A novel augmented complex valued kernel LMS , 2012, 2012 IEEE 7th Sensor Array and Multichannel Signal Processing Workshop (SAM).

[21]  Badong Chen,et al.  Quantized Kernel Recursive Least Squares Algorithm , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[22]  Jie Chen,et al.  Convergence analysis of kernel LMS algorithm with pre-tuned dictionary , 2013, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[23]  Tokunbo Ogunfunmi,et al.  Study of the Convergence Behavior of the Complex Kernel Least Mean Square Algorithm , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[24]  Weifeng Liu,et al.  Kernel Affine Projection Algorithms , 2008, EURASIP J. Adv. Signal Process..

[25]  Jie Chen,et al.  Online Dictionary Learning for Kernel LMS , 2014, IEEE Transactions on Signal Processing.

[26]  Sun-Yuan Kung,et al.  Multikernel Least Mean Square Algorithm , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[27]  Sergios Theodoridis,et al.  Sliding Window Generalized Kernel Affine Projection Algorithm Using Projection Mappings , 2008, EURASIP J. Adv. Signal Process..