On data depth in infinite dimensional spaces
On data depth in infinite dimensional spaces
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DOI：
10.1007/s10463-013-0416-y
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发表时间：
2014-04-01
影响因子：
1
通讯作者：
Chaudhuri, Probal
中科院分区：
文献类型：
--
作者：
Chakraborty, Anirvan;Chaudhuri, Probal
数据深度的概念导致多元数据的中心向外排序，并且它已被有效地用于开发各种数据分析工具。虽然不同的深度概念最初是针对有限维数据开发的，但最近出现了一些尝试为无限维空间中的数据开发深度函数。在本文中，我们考虑无限维空间中的一些深度概念，并研究它们在各种随机模型下的性质。我们的分析表明，文献中可用的一些深度函数对于序列和函数的无限维空间中的一些常用概率分布具有退化行为。因此，它们对于分析满足此类无限维概率模型的数据不是很有用。然而，这些深度函数的一些修改版本以及空间深度的无限维扩展不会遭受这种简并性，并且可以方便地用于分析无限维数据。
The concept of data depth leads to a center-outward ordering of multivariate data, and it has been effectively used for developing various data analytic tools. While different notions of depth were originally developed for finite dimensional data, there have been some recent attempts to develop depth functions for data in infinite dimensional spaces. In this paper, we consider some notions of depth in infinite dimensional spaces and study their properties under various stochastic models. Our analysis shows that some of the depth functions available in the literature have degenerate behaviour for some commonly used probability distributions in infinite dimensional spaces of sequences and functions. As a consequence, they are not very useful for the analysis of data satisfying such infinite dimensional probability models. However, some modified versions of those depth functions as well as an infinite dimensional extension of the spatial depth do not suffer from such degeneracy and can be conveniently used for analyzing infinite dimensional data.