Bootstrapping estimates of stability for clusters, observations and model selection
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Clustering is a challenging problem in unsupervised learning. In lieu of a gold standard, stability has become a valuable surrogate to performance and robustness. In this work, we propose a non-parametric bootstrapping approach to estimating the stability of a clustering method, which also captures stability of the individual clusters and observations. This flexible framework enables different types of comparisons between clusterings and can be used in connection with two possible bootstrap approaches for stability. The first approach, scheme 1, can be used to assess confidence (stability) around clustering from the original dataset based on bootstrap replications. A second approach, scheme 2, searches over the bootstrap clusterings for an optimally stable partitioning of the data. The two schemes accommodate different model assumptions that can be motivated by an investigator’s trust (or lack thereof) in the original data and additional computational considerations. We propose a hierarchical visualization extrapolated from the stability profiles that give insights into the separation of groups, and projected visualizations for the inspection of the stability of individual operations. Our approaches show good performance in simulation and on real data. These approaches can be implemented using the R package bootcluster that is available on the Comprehensive R Archive Network (CRAN).
KeywordsEnsemble k-means Jaccard coefficient Clustering Visualization
- Ben-Hur A, Elisseeff A, Guyon I (2001) A stability based method for discovering structure in clustered data. In: Pacific symposium on biocomputing, vol 7, pp 6–17Google Scholar
- Breiman L (1996) Out-of-bag estimation. Technical report, Statistics Department, University of California Berkeley, Berkeley CAGoogle Scholar
- Efron B, Tibshirani RJ (1994) An Introduction to the bootstrap: Chapman and Hall/CRC monographs on statistics and applied probability. CRC Press, Boca RatonGoogle Scholar
- Ross DT, Scherf U, Eisen MB, Perou CM, Rees C, Spellman P, Iyer V, Jeffrey SS, Van de Rijn M, Waltham M, Permamenschikov L, Lashkari D, Shalon D, Myers T, Botstein D, Brown P (2000) Systematic variation in gene expression patterns in human cancer cell lines. Nat Genet 24(3):227–235CrossRefGoogle Scholar