论文标题
内核中心改编在复制的内核希尔伯特空间嵌入方法中
Kernel Center Adaptation in the Reproducing Kernel Hilbert Space Embedding Method
论文作者
论文摘要
在复制核希尔伯特空间（RKHS）中使用嵌入的自适应估计器的性能取决于基础内核中心的位置的选择。参数收敛和误差近似速率取决于内核中心在状态空间中的分布方式和方式。在本文中，我们开发了将参数收敛和近似速率与内核中心位置相关的理论。我们制定了在特定类别的系统中选择内核中心的标准 - 国家轨迹定期访问正限制集合的附近。基于Centroidal voronoi Tessellations和Kohonen自组织图的两种算法被得出以选择RKHS嵌入方法中的内核中心。最后，我们在两个实际示例上实施这些方法并测试它们的有效性。
The performance of adaptive estimators that employ embedding in reproducing kernel Hilbert spaces (RKHS) depends on the choice of the location of basis kernel centers. Parameter convergence and error approximation rates depend on where and how the kernel centers are distributed in the state-space. In this paper, we develop the theory that relates parameter convergence and approximation rates to the position of kernel centers. We develop criteria for choosing kernel centers in a specific class of systems - ones in which the state trajectory regularly visits the neighborhood of the positive limit set. Two algorithms, based on centroidal Voronoi tessellations and Kohonen self-organizing maps, are derived to choose kernel centers in the RKHS embedding method. Finally, we implement these methods on two practical examples and test their effectiveness.
