论文标题
加权镜头深度：某些用于监督分类的应用
Weighted lens depth: Some applications to supervised classification
论文作者
论文摘要
从Tukey在1970年代的开创性工作开始，统计深度的概念已被广泛扩展，尤其是在过去的十年中。这些扩展包括高维数据，功能数据和歧管值数据。特别是，在学习范式中，深度深度方法已成为一种有用的技术。在本文中，我们将镜头深度的概念扩展到了度量空间中数据的情况，并证明了其主要属性，特别强调了Riemannian歧管的情况，在此，我们以这种方式扩展了镜头深度的概念，以致在数据分布上考虑了非convex结构。接下来，我们通过一些模拟结果以及一些有趣的真实数据集说明了结果，包括使用深度 - 深度方法在系统发育树中的模式识别。
Starting with Tukey's pioneering work in the 1970's, the notion of depth in statistics has been widely extended especially in the last decade. These extensions include high dimensional data, functional data, and manifold-valued data. In particular, in the learning paradigm, the depth-depth method has become a useful technique. In this paper we extend the notion of lens depth to the case of data in metric spaces, and prove its main properties, with particular emphasis on the case of Riemannian manifolds, where we extend the concept of lens depth in such a way that it takes into account non-convex structures on the data distribution. Next we illustrate our results with some simulation results and also in some interesting real datasets, including pattern recognition in phylogenetic trees using the depth--depth approach.
