用超球弦长分布测量空间均匀性
Measuring spatial uniformity with the hypersphere chord length distribution
摘要：
数据一致性是一个与语义数据特征相关的概念，如缺乏特征，相关性和样本偏差。本文介绍了一种新的措施来评估数据的一致性和检测高维欧氏空间上的一致点集。空间均匀性度量建立在超球面弦和L2归一化数据欧氏距离之间的同构基础上，这是由以下事实暗示的：在欧氏空间中，L2归一化数据可以几何地定义为超球面上的点。均匀选点的距离分布和超球面弦长分布之间的强制联系被用来量化均匀性。更具体地说，超球弦长分布的封闭形式的表达式重新访问扩展，在检查一些定性和定量的特点，可以相当直接地链接到数据的均匀性，这个分布。实验部分包括在四个不同的设置中进行验证，从而证实了新的均匀性度量在实际数据科学应用中的潜力。
英文摘要：
Data uniformity is a concept associated with several semantic data characteristics such as lack of features, correlation and sample bias. This article introduces a novel measure to assess data uniformity and detect uniform pointsets on high-dimensional Euclidean spaces. Spatial uniformity measure builds upon the isomorphism between hyperspherical chords and L2-normalised data Euclidean distances, which is implied by the fact that, in Euclidean spaces, L2-normalised data can be geometrically defined as points on a hypersphere. The imposed connection between the distance distribution of uniformly selected points and the hyperspherical chord length distribution is employed to quantify uniformity. More specifically,, the closed-form expression of hypersphere chord length distribution is revisited extended, before examining a few qualitative and quantitative characteristics of this distribution that can be rather straightforwardly linked to data uniformity. The experimental section includes validation in four distinct setups, thus substantiating the potential of the new uniformity measure on practical data-science applications.
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