Pruning nearest neighbor cluster trees
Pruning nearest neighbor cluster trees
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发表时间：
2011-05
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通讯作者：
Samory Kpotufe;U. V. Luxburg
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作者：
Samory Kpotufe;U. V. Luxburg
最近邻 (k-NN) 图广泛应用于机器学习和数据挖掘应用中，我们的目的是更好地理解它们揭示的未知潜在点分布的簇结构。此外，是否有可能识别由于采样变异性而可能出现的虚假结构？我们的第一个贡献是统计分析，揭示了 k-NN 图的某些子图如何形成基础点分布的聚类树的一致估计器。我们的第二个也许是最重要的贡献是以下有限样本保证。我们仔细地权衡了积极修剪和保守修剪之间的关系，并能够保证去除树各级的所有虚假簇结构，同时保证显着簇的恢复。这是聚类背景下第一个此类有限样本结果。
Nearest neighbor (k-NN) graphs are widely used in machine learning and data mining applications, and our aim is to better understand what they reveal about the cluster structure of the unknown underlying distribution of points. Moreover, is it possible to identify spurious structures that might arise due to sampling variability? Our first contribution is a statistical analysis that reveals how certain subgraphs of a k-NN graph form a consistent estimator of the cluster tree of the underlying distribution of points. Our second and perhaps most important contribution is the following finite sample guarantee. We carefully work out the tradeoff between aggressive and conservative pruning and are able to guarantee the removal of all spurious cluster structures at all levels of the tree while at the same time guaranteeing the recovery of salient clusters. This is the first such finite sample result in the context of clustering.