加权透镜深度:在监督分类中的一些应用

IF 0.8 4区 数学 Q3 STATISTICS & PROBABILITY
Alejandro Cholaquidis, Ricardo Fraiman, Fabrice Gamboa, Leonardo Moreno
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引用次数: 6

摘要

从20世纪70年代Tukey的开创性工作开始,统计学中深度的概念得到了广泛的扩展,尤其是在最近十年。这些扩展包括高维数据、函数数据和流形值数据。特别是在学习范式中,深度-深度方法已经成为一种有用的技术。在本文中,我们将透镜深度扩展到度量空间中的数据,并研究了它的主要性质。我们还介绍了黎曼流形的加权透镜深度。加权透镜深度只不过是黎曼距离加权后的透镜深度。为了建立它,我们用费马距离代替流形上的测地线距离,费马距离具有在考虑测地线距离的同时考虑数据密度的重要性质。接下来,我们用一些模拟和一些有趣的真实数据集来说明我们的结果,包括系统发育树中的模式识别,使用深度-深度方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Weighted lens depth: Some applications to supervised classification

Starting with Tukey's pioneering work in the 1970s, the notion of depth in statistics has been widely extended, especially in the last decade. Such extensions include those to 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 article, we extend the lens depth to the case of data in metric spaces and study its main properties. We also introduce, for Riemannian manifolds, the weighted lens depth. The weighted lens depth is nothing more than a lens depth for a weighted version of the Riemannian distance. To build it, we replace the geodesic distance on the manifold with the Fermat distance, which has the important property of taking into account the density of the data together with the geodesic distance. Next, we illustrate our results with some simulations and also in some interesting real datasets, including pattern recognition in phylogenetic trees, using the depth-depth approach.

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来源期刊
CiteScore
1.40
自引率
0.00%
发文量
62
审稿时长
>12 weeks
期刊介绍: The Canadian Journal of Statistics is the official journal of the Statistical Society of Canada. It has a reputation internationally as an excellent journal. The editorial board is comprised of statistical scientists with applied, computational, methodological, theoretical and probabilistic interests. Their role is to ensure that the journal continues to provide an international forum for the discipline of Statistics. The journal seeks papers making broad points of interest to many readers, whereas papers making important points of more specific interest are better placed in more specialized journals. The levels of innovation and impact are key in the evaluation of submitted manuscripts.
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