Wirtinger演算在RKH空间中的推广及复核LMS
Extension of Wirtinger Calculus in RKH Spaces and the Complex Kernel LMS
摘要：
在过去的十年中，非线性处理的核方法已成功地用于机器学习社区。然而，到目前为止，重点一直放在批处理技术上。直到最近，在线自适应技术已被认为是在信号处理任务的背景下。据我们所知，到目前为止，还没有开发出能够处理复值信号的基于内核的策略。在本文中，我们利用一种技术称为复杂化的真正RKHS攻击这个问题。为了得到梯度和子梯度的运营商，需要定义在相关的复杂RKHS，我们采用了强大的工具Wirtinger的微积分，这是最近引起了人们的关注，在信号处理社区。辛格的微积分简化了计算，为处理复杂信号提供了一个优雅的工具。为此，在本文中，的概念扩展到，第一次，包括复杂的RKHS，并使用它来推导复杂的核最小均方（CKLMS）算法。实验证明，CKLMS算法可以用于非线性稳定算法，在处理非线性问题时，其性能优于传统的复数LMS算法和宽线性复数LMS（WL-LMS）算法。
英文摘要：
Over the last decade, kernel methods for nonlinear processing have successfully been used in the machine learning community. However, so far, the emphasis has been on batch techniques. It is only recently, that online adaptive techniques have been considered in the context of signal processing tasks. To the best of our knowledge, no kernel-based strategy has been developed, so far, that is able to deal with complex valued signals. In this paper, we take advantage of a technique called complexification of real RKHSs to attack this problem. In order to derive gradients and subgradients of operators that need to be defined on the associated complex RKHSs, we employ the powerful tool ofWirtinger's Calculus, which has recently attracted much attention in the signal processing community. Writinger's calculus simplifies computations and offers an elegant tool for treating complex signals. To this end, in this paper, the notion of Writinger's calculus is extended, for the first time, to include complex RKHSs and use it to derive the Complex Kernel Least-Mean-Square (CKLMS) algorithm. Experiments verify that the CKLMS can be used to derive nonlinear stable algorithms, which offer significant performance improvements over the traditional complex LMS orWidely Linear complex LMS (WL-LMS) algorithms, when dealing with nonlinearities.
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