Goh Su Lee, Mandic Danilo P
Imperial College London, Exhibition Road, London SW7 2AZ, United
Neural Netw. 2007 Dec;20(10):1061-6. doi: 10.1016/j.neunet.2007.09.015. Epub 2007 Sep 22.
Real world processes with an "intensity" and "direction" component can be made complex by convenience of representation (vector fields, radar, sonar), and their processing directly in the field of complex numbers C is not only natural but is also becoming commonplace in modern applications. Yet, adaptive signal processing and machine learning algorithms suitable for the processing of such signals directly in C are only emerging. To this cause we introduce a second order statistical learning framework for a general class of nonlinear adaptive filters with feedback realized as recurrent neural networks (RNNs). For rigour, both the so-called proper- and improper-second order statistics of complex processes is taken into account, and the proposed augmented complex real-time recurrent learning (ACRTRL) algorithm for RNNs has been shown to be suitable for processing a wide range of both benchmark and real-world complex processes.
具有“强度”和“方向”分量的现实世界过程，由于表示方式（向量场、雷达、声纳）的便利性而变得复杂，并且直接在复数域C中对其进行处理不仅很自然，而且在现代应用中也变得越来越普遍。然而，适用于直接在C中处理此类信号的自适应信号处理和机器学习算法才刚刚出现。为此，我们为一类通过递归神经网络（RNN）实现反馈的非线性自适应滤波器引入了二阶统计学习框架。为了严谨起见，我们考虑了复过程的所谓恰当和非恰当二阶统计量，并且已证明所提出的用于RNN的增强型复实时递归学习（ACRTRL）算法适用于处理广泛的基准和现实世界的复杂过程。
