Out-of-bag stability estimation for k-means clustering

Clustering data is a challenging problem in unsupervised learning where there is no gold standard. Results depend on several factors, such as the selection of a clustering method, measures of dissimilarity, parameters, and the determination of the number of reliable groupings. Stability has become a valuable surrogate to performance and robustness that can provide insight to an investigator on the quality of a clustering, and guidance on subsequent cluster prioritization. This work develops a framework for stability measurements that is based on resampling and OB estimation. Bootstrapping methods for cluster stability can be prone to overfitting in a setting that is analogous to poor delineation of test and training sets in supervised learning. Stability that relies on OB items from a resampling overcomes these issues and does not depend on a reference clustering for comparisons. Furthermore, OB stability can provide estimates at the level of the item, cluster, and as an overall summary, which has good interpretive value. This framework is extended to develop stability estimates for determining the number of clusters (model selection) through contrasts between stability estimates on clustered data, and stability estimates of clustered reference data with no signal. These contrasts form stability profiles that can be used to identify the largest differences in stability and do not require a direct threshold on stability values, which tend to be data specific. These approaches can be implemented using the R package bootcluster that is available on the Comprehensive R Archive Network.