We consider the problem of estimating the number of clusters ($k$) in a dataset. We propose a non-parametric approach to the problem that is based on maximizing a statistic constructed from similarity graphs. This graph-based statistic is a robust summary measure of the similarity information among observations and is applicable even if the number of dimensions or number of clusters is possibly large. The approach is straightforward to implement, computationally fast, and can be paired with any kind of clustering technique. Asymptotic theory is developed to establish the selection consistency of the proposed approach. Simulation studies demonstrate that the graph-based statistic outperforms existing methods for estimating $k$. We illustrate its utility on a high-dimensional image dataset and RNA-seq dataset.

翻译：我们考虑数据集中聚类数量（$k$）的估计问题。提出一种非参数方法，通过最大化基于相似性图构建的统计量来估计聚类数。该图基统计量是观测值间相似性信息的稳健汇总度量，即使在维度或聚类数量可能较大的情况下仍适用。该方法实现简单、计算高效，可与任意聚类技术配对使用。通过渐进理论分析验证了所提方法的相合性，模拟研究表明该图基统计量在估计$k$时优于现有方法。我们在高维图像数据集和RNA-seq数据集上展示了其实用性。