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arXiv 2602.16673cs.LGcs.IR
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邻域稳定性作为最近邻搜索性的度量

Neighborhood Stability as a Measure of Nearest Neighbor Searchability

University of Copenhagen, Copenhagen, Denmark(哥本哈根大学);Northeastern University, Boston, MA, USA(东北大学)

Thomas Vecchiato, Sebastian Bruch

AI总结:

本文提出两种度量方法,用于评估数据集是否可通过基于聚类的近似最近邻搜索进行搜索,且不依赖特定距离函数。

摘要:

基于聚类的近似最近邻搜索(ANNS)将一组点划分为若干分区,并仅搜索其中少数几个分区来查找查询点的最近邻。尽管其普及度很高,但几乎没有分析工具可以确定聚类-based ANNS对于特定数据集的适用性——这是我们所说的“搜索性”。为填补这一空白,我们提出了两种针对高维点在欧几里得空间中扁平聚类的度量方法。第一种是聚类-邻域稳定性度量(clustering-NSM),一种聚类质量的内部度量——一个数据集聚类的函数——我们证明其能够预测ANNS的准确性。第二种是点-邻域稳定性度量(point-NSM),一种聚类性的度量——一个数据集本身的函数——能够预测聚类-NSM。两者共同允许我们仅凭数据点确定数据集是否可以通过基于聚类的ANNS进行搜索。重要的是,两者都是基于点之间的最近邻关系,而非距离,使其适用于各种距离函数,包括内积。

英文摘要:

Clustering-based Approximate Nearest Neighbor Search (ANNS) organizes a set of points into partitions, and searches only a few of them to find the nearest neighbors of a query. Despite its popularity, there are virtually no analytical tools to determine the suitability of clustering-based ANNS for a given dataset -- what we call "searchability." To address that gap, we present two measures for flat clusterings of high-dimensional points in Euclidean space. First is Clustering-Neighborhood Stability Measure (clustering-NSM), an internal measure of clustering quality -- a function of a clustering of a dataset -- that we show to be predictive of ANNS accuracy. The second, Point-Neighborhood Stability Measure (point-NSM), is a measure of clusterability -- a function of the dataset itself -- that is predictive of clustering-NSM. The two together allow us to determine whether a dataset is searchable by clustering-based ANNS given only the data points. Importantly, both are functions of nearest neighbor relationships between points, not distances, making them applicable to various distance functions including inner product.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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