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
