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Effects of Resampling in Determining the Number of Clusters in a Data Set

Author

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  • Rainer Dangl

    (University of Natural Resources and Life Sciences)

  • Friedrich Leisch

    (University of Natural Resources and Life Sciences)

Abstract

Using cluster validation indices is a widely applied method in order to detect the number of groups in a data set and as such a crucial step in the model validation process in clustering. The study presented in this paper demonstrates how the accuracy of certain indices can be significantly improved when calculated numerous times on data sets resampled from the original data. There are obviously many ways to resample data—in this study, three very common options are used: bootstrapping, data splitting (without subset overlap of two subsamples), and random subsetting (with subset overlap of two subsamples). Index values calculated on the basis of resampled data sets are compared to the values obtained from the original data partition. The primary hypothesis of the study states that resampling does generally improve index accuracy. The hypothesis is based on the notion of cluster stability: if there are stable clusters in a data set, a clustering algorithm should produce consistent results for data sampled or resampled from the same source. The primary hypothesis was partly confirmed; for external validation measures, it does indeed apply. The secondary hypothesis states that the resampling strategy itself does not play a significant role. This was also shown to be accurate, yet slight deviations between the resampling schemes suggest that splitting appears to yield slightly better results.

Suggested Citation

  • Rainer Dangl & Friedrich Leisch, 2020. "Effects of Resampling in Determining the Number of Clusters in a Data Set," Journal of Classification, Springer;The Classification Society, vol. 37(3), pages 558-583, October.
    • Handle: RePEc:spr:jclass:v:37:y:2020:i:3:d:10.1007_s00357-019-09328-2
    DOI: 10.1007/s00357-019-09328-2
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    References listed on IDEAS

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    1. Weiliang Qiu & Harry Joe, 2006. "Generation of Random Clusters with Specified Degree of Separation," Journal of Classification, Springer;The Classification Society, vol. 23(2), pages 315-334, September.
    2. Robert Tibshirani & Guenther Walther & Trevor Hastie, 2001. "Estimating the number of clusters in a data set via the gap statistic," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 411-423.
    3. Evgenia Dimitriadou & Sara Dolničar & Andreas Weingessel, 2002. "An examination of indexes for determining the number of clusters in binary data sets," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 137-159, March.
    4. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    5. Leisch, Friedrich, 2006. "A toolbox for K-centroids cluster analysis," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 526-544, November.
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