Title :
Study of the Convergence Behavior of the Complex Kernel Least Mean Square Algorithm
Author :
Paul, Thomas K. ; Ogunfunmi, Tokunbo
Author_Institution :
Dept. of Electr. Eng., Santa Clara Univ., Santa Clara, CA, USA
Abstract :
The complex kernel least mean square (CKLMS) algorithm is recently derived and allows for online kernel adaptive learning for complex data. Kernel adaptive methods can be used in finding solutions for neural network and machine learning applications. The derivation of CKLMS involved the development of a modified Wirtinger calculus for Hilbert spaces to obtain the cost function gradient. We analyze the convergence of the CKLMS with different kernel forms for complex data. The expressions obtained enable us to generate theory-predicted mean-square error curves considering the circularity of the complex input signals and their effect on nonlinear learning. Simulations are used for verifying the analysis results.
Keywords :
Hilbert spaces; adaptive filters; calculus; convergence of numerical methods; gradient methods; learning (artificial intelligence); least mean squares methods; nonlinear filters; statistical analysis; CKLMS; Hilbert spaces; complex kernel least mean square algorithm; convergence behavior; cost function gradient; kernel-based nonlinear adaptive filtering algorithm; modified Wirtinger calculus; nonlinear learning; online kernel adaptive learning; theory-predicted mean-square error curves; Adaptive filters; Gaussian kernel; complex kernel least mean square; complexified; mean-square error; steady-state analysis;
Journal_Title :
Neural Networks and Learning Systems, IEEE Transactions on
DOI :
10.1109/TNNLS.2013.2256367
