Robust Adaptive Generalized Correntropy-based Smoothed Graph Signal Recovery with a Kernel Width Learning

Abstract

This paper proposes a robust adaptive algorithm for smooth graph signal recovery which is based on generalized correntropy. A proper cost function is defined, which takes the smoothness and generalized correntropy into account. The generalized correntropy used in this paper employs the generalized Gaussian density (GGD) function as the kernel. The proposed adaptive algorithm is derived and a kernel width learning-based version of the algorithm is suggested. The simulation results confirm the performance of the proposed algorithm for learning the kernel-width to the fixed correntropy kernel version of the algorithm. Moreover, some theoretical analysis of the proposed algorithm are provided. In this regard, firstly, the convexity analysis of the cost function is discussed. Secondly, the uniform stability of the algorithm is investigated. Thirdly, the mean convergence analysis is also added. Finally, the computational complexity analysis of the algorithm is incorporated. In addition, some synthetic and real-world experiments show the efficiency of the proposed algorithm in comparison to some other adaptive algorithms in the literature of adaptive graph signal recovery.