Nonlinear similarity measures defined in kernel space, such as correntropy, can extract higher-order statistics of data and offer potentially significant performance improvement over their linear counterparts especially in non-Gaussian signal processing and machine learning. In this work, we propose a new similarity measure in kernel space, called the kernel risk-sensitive loss (KRSL), and provide some important properties. We apply the KRSL to adaptive filtering and investigate the robustness, and then develop the MKRSL algorithm and analyze the mean square convergence performance. Compared with correntropy, the KRSL can offer a more efficient performance surface, thereby enabling a gradient based method to achieve faster convergence speed and higher accuracy while still maintaining the robustness to outliers. Theoretical analysis results and superior performance of the new algorithm are confirmed by simulation.
Spectral Equivariance and Geometric Transport in Reproducing Kernel Hilbert Spaces: A Unified Framework for Orthogonal Polynomial and Kernel Estimation
估计再生核希尔伯特空间（RKHS）中的核均值的问题是核方法的核心，因为它被经典方法（例如，当将核PCA矩阵居中时），并且它还形成现代核方法的核心推理步骤（例如，基于核的非参数检验），其依赖于在RKHS中嵌入概率分布。Muandet等人（2014）已经表明，收缩可以帮助构建比经验估计量“更好”的核均值估计量。本文研究了Muandet et al.（2014）中估计量的相容性和可容许性，并提出了一类更广泛的收缩估计量，通过考虑适当的基函数来改进经验估计量。使用核PCA的基础上，我们表明，这些估计可以使用频谱滤波算法，这是一致的，在一些技术假设。我们的理论分析还揭示了与基于内核的监督学习框架的基本联系。建议的估计是简单的实现和执行良好的实践。
Asymmetric Correntropy for Robust Adaptive Filtering
Xi’an Jiaotong University（西安交通大学）；Xi’an Microelectronic Technology Institute（西安微电子技术研究所）；Harbin Engineering University（哈尔滨工程大学）；National Space Science Center, Chinese Academy of Sciences（中国科学院国家空间科学中心）
Rotation-Parameterized Graph Fractional Fourier Transform: Definition, Properties, and Optimal Filtering
School of Mathematics and Statistics, Nanjing University of Information Science and Technology（南京信息工程大学数学与统计学院）；School of Communication and Artificial Intelligence, Nanjing Institute of Technology（南京理工大学通信与人工智能学院）；School of Integrated Circuits, Nanjing Institute of Technology（南京理工大学集成电路学院）；Jiangsu Province Engineering Research Center of IntelliSense Technology and System（江苏省智能感知技术与系统工程研究中心）；Hubei Key Laboratory of Applied Mathematics, Hubei University（湖北省应用数学重点实验室）；Key Laboratory of System Control and Information Processing, Ministry of Education, Shanghai Jiao Tong University（教育部系统控制与信息处理重点实验室，上海交通大学）
