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Bisecting K-Means and 1D Projection Divisive Clustering: A Unified Framework and Experimental Comparison

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  • Ekaterina Kovaleva
  • Boris Mirkin

Abstract

The paper presents a least squares framework for divisive clustering. Two popular divisive clustering methods, Bisecting K-Means and Principal Direction Division, appear to be versions of the same least squares approach. The PDD recently has been enhanced with a stopping criterion taking into account the minima of the corresponding one-dimensional density function (dePDDP method). We extend this approach to Bisecting K-Means by projecting the data onto random directions and compare thus modified methods. It appears the dePDDP method is superior at datasets with relatively small numbers of clusters, whatever cluster intermix, whereas our version of Bisecting K-Means is superior at greater cluster numbers with noise entities added to the cluster structure. Copyright Classification Society of North America 2015

Suggested Citation

  • Ekaterina Kovaleva & Boris Mirkin, 2015. "Bisecting K-Means and 1D Projection Divisive Clustering: A Unified Framework and Experimental Comparison," Journal of Classification, Springer;The Classification Society, vol. 32(3), pages 414-442, October.
    • Handle: RePEc:spr:jclass:v:32:y:2015:i:3:p:414-442
    DOI: 10.1007/s00357-015-9186-y
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    References listed on IDEAS

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    1. Mark Chiang & Boris Mirkin, 2010. "Intelligent Choice of the Number of Clusters in K-Means Clustering: An Experimental Study with Different Cluster Spreads," Journal of Classification, Springer;The Classification Society, vol. 27(1), pages 3-40, March.
    2. Douglas Steinley & Michael J. Brusco, 2007. "Initializing K-means Batch Clustering: A Critical Evaluation of Several Techniques," Journal of Classification, Springer;The Classification Society, vol. 24(1), pages 99-121, June.
    3. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    4. Meila, Marina, 2007. "Comparing clusterings--an information based distance," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 873-895, May.
    5. Ahmed N. Albatineh & Magdalena Niewiadomska-Bugaj & Daniel Mihalko, 2006. "On Similarity Indices and Correction for Chance Agreement," Journal of Classification, Springer;The Classification Society, vol. 23(2), pages 301-313, September.
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    Cited by:

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    2. Boris Mirkin & Soroosh Shalileh, 2022. "Community Detection in Feature-Rich Networks Using Data Recovery Approach," Journal of Classification, Springer;The Classification Society, vol. 39(3), pages 432-462, November.

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