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Strong consistency of k-parameters clustering

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  • Gallegos, María Teresa
  • Ritter, Gunter

Abstract

Pollard showed for k-means clustering and a very broad class of sampling distributions that the optimal cluster means converge to the solution of the related population criterion as the size of the data set increases. We extend this consistency result to k-parameters clustering, a method derived from the heteroscedastic, elliptical classification model. It allows a more sensitive data analysis and has the advantage of being affine equivariant. Moreover, the present theory yields a consistent criterion for selecting the number of clusters in such models.

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  • Gallegos, María Teresa & Ritter, Gunter, 2013. "Strong consistency of k-parameters clustering," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 14-31.
    • Handle: RePEc:eee:jmvana:v:117:y:2013:i:c:p:14-31
    DOI: 10.1016/j.jmva.2013.01.013
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    References listed on IDEAS

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    Cited by:

    1. María Teresa Gallegos & Gunter Ritter, 2018. "Probabilistic clustering via Pareto solutions and significance tests," 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. 12(2), pages 179-202, June.
    2. Chakraborty, Saptarshi & Das, Swagatam, 2021. "On uniform concentration bounds for Bi-clustering by using the Vapnik–Chervonenkis theory," Statistics & Probability Letters, Elsevier, vol. 175(C).

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