IEEE Trans Neural Netw Learn Syst. 2018 Dec;29(12):6123-6131. doi: 10.1109/TNNLS.2018.2826442. Epub 2018 May 1.
In this paper, kurtosis-based complex-valued real-time recurrent learning (KCRTRL) and kurtosis-based augmented CRTRL (KACRTRL) algorithms are proposed for training fully connected recurrent neural networks (FCRNNs) in the complex domain. These algorithms are designed by minimizing the cost functions based on the kurtosis of a complex-valued error signal. The KCRTRL algorithm exploits the circularity properties of the complex-valued signals, and this algorithm not only provides a faster convergence rate but also results in a lower steady-state error. However, the KCRTRL algorithm is suboptimal in the processing of noncircular (NC) complex-valued signals. On the other hand, the KACRTRL algorithm contains a complete second-order information due to the augmented statistics, thus considerably improves the performance of the FCRNN in the processing of NC complex-valued signals. Simulation results on the one-step-ahead prediction problems show that the proposed KCRTRL algorithm significantly enhances the performance for only circular complex-valued signals, whereas the proposed KACRTRL algorithm provides more superior performance than existing algorithms for NC complex-valued signals in terms of the convergence rate and the steady-state error.
本文提出了基于峰度的复值实时递归学习（KCRTRL）和基于峰度的增广 CRTRL（KACRTRL）算法，用于在复域中训练全连接递归神经网络（FCRNN）。这些算法通过基于复值误差信号的峰度最小化代价函数来设计。KCRTRL 算法利用了复值信号的圆性特性，该算法不仅提供了更快的收敛速度，而且还导致了更低的稳态误差。然而，KCRTRL 算法在处理非圆（NC）复值信号时是次优的。另一方面，KACRTRL 算法由于增广的统计信息而包含完整的二阶信息，因此大大提高了 FCRNN 在处理 NC 复值信号时的性能。在一步预测问题上的仿真结果表明，所提出的 KCRTRL 算法仅显著增强了仅对圆复值信号的性能，而所提出的 KACRTRL 算法在收敛速度和稳态误差方面为 NC 复值信号提供了比现有算法更优越的性能。
