High-Dimensional Simplexes for Supermetric Search
High-Dimensional Simplexes for Supermetric Search
复制标题
用于超度量搜索的高维单纯形
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
F. Rabitti
中科院分区：
文献类型：
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作者：
R. Connor;Lucia Vadicamo;F. Rabitti
在度量空间中，三角不等式意味着，对于任意三个物体，都可以形成一个边长与其两两距离相对应的三角形。N点性质是这一性质的推广，其中对于空间中的任何((n+1)个)对象，存在其边长对应于对象之间的距离的n维单形。一般而言，度量空间不具有这一性质；然而，1953年，Blumenthal证明了任何等距可嵌入到Hilbert空间中的半度量空间也具有n点性质。
In a metric space, triangle inequality implies that, for any three objects, a triangle with edge lengths corresponding to their pairwise distances can be formed. The n-point property is a generalisation of this where, for any ((n+1)) objects in the space, there exists an n-dimensional simplex whose edge lengths correspond to the distances among the objects. In general, metric spaces do not have this property; however in 1953, Blumenthal showed that any semi-metric space which is isometrically embeddable in a Hilbert space also has the n-point property.