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Initializing k-means Clustering by Bootstrap and Data Depth

Author

Listed:
  • Aurora Torrente

    (Universidad Carlos III de Madrid)

  • Juan Romo

    (Universidad Carlos III de Madrid)

Abstract

The k-means algorithm is widely used in various research fields because of its fast convergence to the cost function minima; however, it frequently gets stuck in local optima as it is sensitive to initial conditions. This paper explores a simple, computationally feasible method, which provides k-means with a set of initial seeds to cluster datasets of arbitrary dimensions. Our technique consists of two stages: firstly, we use the original data space to obtain a set of prototypes (cluster centers) by applying k-means to bootstrap replications of the data and, secondly, we cluster the space of centers, which has tighter (thus easier to separate) groups, and search the deepest point in each assembled cluster using a depth notion. We test this method with simulated and real data, compare it with commonly used k-means initialization algorithms, and show that it is feasible and more efficient than previous proposals in many situations.

Suggested Citation

  • Aurora Torrente & Juan Romo, 2021. "Initializing k-means Clustering by Bootstrap and Data Depth," Journal of Classification, Springer;The Classification Society, vol. 38(2), pages 232-256, July.
    • Handle: RePEc:spr:jclass:v:38:y:2021:i:2:d:10.1007_s00357-020-09372-3
    DOI: 10.1007/s00357-020-09372-3
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    References listed on IDEAS

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    1. Glenn Milligan & Martha Cooper, 1988. "A study of standardization of variables in cluster analysis," Journal of Classification, Springer;The Classification Society, vol. 5(2), pages 181-204, September.
    2. Joeri Hofmans & Eva Ceulemans & Douglas Steinley & Iven Mechelen, 2015. "On the Added Value of Bootstrap Analysis for K-Means Clustering," Journal of Classification, Springer;The Classification Society, vol. 32(2), pages 268-284, July.
    3. López-Pintado, Sara & Romo, Juan, 2009. "On the Concept of Depth for Functional Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 718-734.
    4. Daniel Aloise & Nielsen Castelo Damasceno & Nenad Mladenović & Daniel Nobre Pinheiro, 2017. "On Strategies to Fix Degenerate k-means Solutions," Journal of Classification, Springer;The Classification Society, vol. 34(2), pages 165-190, July.
    5. Oja, Hannu, 1983. "Descriptive statistics for multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 1(6), pages 327-332, October.
    6. 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.
    7. Hennig, Christian, 2007. "Cluster-wise assessment of cluster stability," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 258-271, September.
    8. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    9. Glenn Milligan, 1980. "An examination of the effect of six types of error perturbation on fifteen clustering algorithms," Psychometrika, Springer;The Psychometric Society, vol. 45(3), pages 325-342, September.
    10. Michael Brusco & J. Cradit, 2001. "A variable-selection heuristic for K-means clustering," Psychometrika, Springer;The Psychometric Society, vol. 66(2), pages 249-270, June.
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    Cited by:

    1. Giuseppe Pandolfo & Antonio D’ambrosio, 2023. "Clustering directional data through depth functions," Computational Statistics, Springer, vol. 38(3), pages 1487-1506, September.
    2. Javier Albert-Smet & Aurora Torrente & Juan Romo, 2023. "Band depth based initialization of K-means for functional data clustering," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(2), pages 463-484, June.

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