In kernel methods, the median heuristic has been widely used as a way of
setting the bandwidth of RBF kernels. While its empirical performances make it
a safe choice under many circumstances, there is little theoretical
understanding of why this is the case. Our aim in this paper is to advance our
understanding of the median heuristic by focusing on the setting of kernel
two-sample test. We collect new findings that may be of interest for both
theoreticians and practitioners. In theory, we provide a convergence analysis
that shows the asymptotic normality of the bandwidth chosen by the median
heuristic in the setting of kernel two-sample test. Systematic empirical
investigations are also conducted in simple settings, comparing the
performances based on the bandwidths chosen by the median heuristic and those
by the maximization of test power.

该研究通过对核二样本检验的带宽设置进行收集新的发现，提供渐近正态性的收敛分析，比较了基于中值启发式和测试功率最大化选择的带宽的性能。

中位数启发式算法的大样本分析

Large sample analysis of the median heuristic

In this paper, we explore tensor representations that can compactly capture
higher-order relationships between skeleton joints for 3D action recognition.
We first define RBF kernels on 3D joint sequences, which are then linearized to
form kernel descriptors. The higher-order outer-products of these kernel
descriptors form our tensor representations. We present two different kernels
for action recognition, namely (i) a sequence compatibility kernel that
captures the spatio-temporal compatibility of joints in one sequence against
those in the other, and (ii) a dynamics compatibility kernel that explicitly
models the action dynamics of a sequence. Tensors formed from these kernels are
then used to train an SVM. We present experiments on several benchmark datasets
and demonstrate state of the art results, substantiating the effectiveness of
our representations.

本文提出了一种基于张量表示的三维动作识别方法，使用径向基函数 (RBF) 生成核描述符，通过描述符的高阶外积形成张量表示，同时使用序列兼容性核和动态兼容性核进行动作识别，该方法在多个基准数据集上实现了最好的效果。