IEEE Trans Neural Netw Learn Syst. 2013 Sep;24(9):1349-63. doi: 10.1109/TNNLS.2013.2256367.
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.
复杂核最小均方（CKLMS）算法是最近推导出来的，允许对复数据进行在线核自适应学习。核自适应方法可用于寻找神经网络和机器学习应用的解决方案。CKLMS 的推导涉及到为 Hilbert 空间开发一个改进的 Wirtinger 微积分，以获得代价函数梯度。我们分析了不同核形式的 CKLMS 在复数据下的收敛性。所得到的表达式使我们能够生成理论预测的均方误差曲线，考虑到复输入信号的圆性及其对非线性学习的影响。模拟用于验证分析结果。
