On the Nearest Neighbor of the Nearest Neighbor in Multidimensional Continuous and Quantized Space

Rovatti R.; Mazzini G.

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On the Nearest Neighbor of the Nearest Neighbor in Multidimensional Continuous and Quantized Space

机译：关于多维连续量化空间中最近邻居的最近邻居

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摘要

The probability that an entity in a set of entities uniformly distributed in space is the nearest neighbor of its nearest neighbor is evaluated for generic distances in a multidimensional environment. Such an expression is then specialized for systems with norm-based distances and for systems with quantized norm- based distance. Examples for scalar products and sup-norm are derived. When applicable, invariances with respect to the underlying distance and entities density are highlighted. Dimensionality effects are investigated.

机译：针对多维环境中的一般距离，评估在空间上均匀分布的一组实体中的一个实体是其最近邻居的概率。然后，这样的表达式专用于具有基于规范的距离的系统和具有量化的基于规范的距离的系统。导出标量积和sup-norm的示例。如果适用，突出显示有关基础距离和实体密度的不变性。研究了尺寸效应。

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来源
《IEEE Transactions on Information Theory》 |2008年第9期|p.4069-4080|共12页
作者
Rovatti R.; Mazzini G.;
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正文语种 eng
中图分类无线电电子学、电信技术;
关键词
information theory; dimensionality effects; entity; multidimensional continuous space; multidimensional quantized space; norm-based distances; Dimensionality effect; Euclidean distances; Poisson point processes; nearest neighbor; quantized distances;

机译：信息论;维数效应;实体;多维连续空间;多维量化空间;基于范数的距离;维数效应;欧氏距离;泊松点过程;近邻;量化距离;

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2. Nearest Neighbors and Continuous Nearest Neighbor Queries based on Voronoi Diagrams [J] . Miao Wang, Zhongxiao Hao Information Technology Journal . 2010,第7期

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On the Nearest Neighbor of the Nearest Neighbor in Multidimensional Continuous and Quantized Space

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