In this article, we introduce a general framework of angle based independence test using reproducing kernel Hilbert space. We consider that both random variables are in metric spaces. By making use of the reproducing kernel Hilbert space equipped with Gaussian measure, we derive the angle based dependence measures with simple and explicit forms. This framework can be adapted to different types of data, like high-dimensional vectors or symmetry positive definite matrices. And it also incorporates several well-known angle based independence tests. In addition, our framework can induce another notable dependence measure, generalized distance correlation, which is proposed by direct definition. We conduct comprehensive simulations on various types of data, including large dimensional vectors and symmetry positive definite matrix, which shows remarkable performance. An application of microbiome dataset, characterized with high dimensionality, is implemented.

翻译：在本篇文章中,我们引入了一个利用复制内核Hilbert空间进行角基独立测试的一般框架。 我们认为,这两个随机变量都存在于多维空间中。 通过利用带有高斯测量的内核Hilbert空间的再生,我们以简单和清晰的形式得出基于角的依附措施。这个框架可以适应不同类型的数据,如高维矢量或对称正确定矩阵。它还包括一些众所周知的以角为基础的独立测试。此外,我们的框架还可以产生另一个显著的依附措施,即由直接定义提出的普遍距离相关性。我们对各种类型的数据进行全面模拟,包括大型向量和对称肯定矩阵,显示显著的性能。还实施了具有高维度特征的微生物数据集的应用。