Internal measures that are used to assess the quality of a clustering usually
take into account intra-group and/or inter-group criteria. There are many
papers in the literature that propose algorithms with provable approximation
guarantees for optimizing the former. However, the optimization of inter-group
criteria is much less understood.
Here, we contribute to the state-of-the-art of this literature by devising
algorithms with provable guarantees for the maximization of two natural
inter-group criteria, namely the minimum spacing and the minimum spanning tree
spacing. The former is the minimum distance between points in different groups
while the latter captures separability through the cost of the minimum spanning
tree that connects all groups. We obtain results for both the unrestricted
case, in which no constraint on the clusters is imposed, and for the
constrained case where each group is required to have a minimum number of
points. Our constraint is motivated by the fact that the popular Single
Linkage, which optimizes both criteria in the unrestricted case, produces
clusterings with many tiny groups.
To complement our work, we present an empirical study with 10 real datasets,
providing evidence that our methods work very well in practical settings.

我们提出了能够最大化两个自然的距离度量准则（最小间距和最小生成树间距）的算法，并且对无限制情况和有约束情况均给出了结果。我们的方法在实际应用中表现非常好，并通过 10 个真实数据集的经验研究提供了证据。