A Bayesian criterion for cluster stability

Abstract

We present a technique for evaluating and comparing how clusterings reveal structure inherent in the data set. Our technique is based on a criterion evaluating how much point-to-cluster distances may be perturbed without affecting the membership of the points. Although similar to some existing perturbation methods, our approach distinguishes itself in five ways. First, the strength of the perturbations is indexed by a prior distribution controlling how close to boundary regions a point may be before it is considered unstable. Second, our approach is exact in that we integrate over all the perturbations; in practice, this can be done efficiently for well-chosen prior distributions. Third, we provide a rigorous theoretical treatment of the approach, showing that it is consistent for estimating the correct number of clusters. Fourth, it yields a detailed picture of the behavior and structure of the clustering. Finally, it is computationally tractable and easy to use, requiring only a point-to-cluster distance matrix as input. In a simulation study, we show that it outperforms several existing methods in terms of recovering the correct number of clusters. We also illustrate the technique in three real data sets.

Using R Packages for Comparison of Cluster Stability

“…There are other new methods proposed which can be found, for example, in the works of: Granichin et al (2015), Hosein et al (2011), Koepke, Clarke (2013) and Ryazanov (2016).…”

Generalized k-means in GLMs with applications to the outbreak of COVID-19 in the United States

“…Notice that many penalties could be used to determine the number of clusters and the gap statistic was just one of those. Examples can be found in Koepke and Clarke (2013) . To know whether the performance of our competitors could be significantly improved if other penalties were adopted, we compared our BIC selector based on an unknown with our competitors based on a known .…”

Optimal transport, mean partition, and uncertainty assessment in cluster analysis

“…This method is called resampling, a thorough review of which is provided by Leisch . Koepke and Clarke provide a broad introduction to different categories of methods for measuring stability. We hereby call an overall clustering result a partition .…”

“…Luxburg provides a nice overview. Koepke and Clarke proposed a Bayesian criterion for evaluating cluster stability. Their idea is distinct because the perturbation of clustering is not performed by resampling but rather by introducing a nonnegative scaling parameter for each cluster.…”

“…Most of the existing work addresses stability at the level of partition. The work of Koepke and Clarke is an exception as the stability can be computed at the levels of individual points, clusters, or overall partitions. More recently, Yu et al also proposed to measure stability at the three levels using bootstrap resampling.…”