Abstract We study the problem of clustering validation, i.e., clustering evaluation without knowledge of ground-truth labels, for the increasingly-popular framework known as subspace clustering. Existing clustering quality metrics (CQMs) rely heavily on a notion of distance between points, but common metrics fail to capture the geometry of subspace clustering. We propose a novel point-to-point pseudometric for points lying on a union of subspaces and show how this allows for the application of existing CQMs to the subspace clustering problem. We provide theoretical and empirical justification for the proposed point-to-point distance, and then demonstrate on a number of common benchmark datasets that our proposed methods generally outperform existing graph-based CQMs in terms of choosing the best clustering and the number of clusters.

中文翻译：

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子空间聚类的聚类质量度量

摘要 我们研究了聚类验证问题，即在不了解真实标签的情况下对日益流行的子空间聚类框架进行聚类评估。现有的聚类质量度量 (CQM) 严重依赖于点之间的距离概念，但常见的度量无法捕捉子空间聚类的几何形状。我们为位于子空间联合上的点提出了一种新颖的点对点伪度量，并展示了这如何允许将现有的 CQM 应用于子空间聚类问题。我们为所提出的点对点距离提供理论和经验证明，然后在许多常见的基准数据集上证明我们提出的方法在选择最佳聚类和聚类数量方面通常优于现有的基于图的 CQM。