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Good (K-means) clusterings are unique (up to small perturbations)

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  • Meilă, Marina

Abstract

If we have found a “good” clustering C of a data set, can we prove that C is not far from the (unknown) best clustering Copt of these data? Perhaps surprisingly, the answer to this question is sometimes yes. This paper gives spectral bounds on the distance d(C,Copt) for the case when “goodness” is measured by a quadratic cost, such as the squared distortion of K-means clustering or the Normalized Cut criterion of spectral clustering. The bounds exist only if the data admit a “good”, low-cost clustering. The results in this paper are non-asymptotic and model-free, in the sense that no assumptions are made on the data generating process. The bounds do not depend on undefined constants, and can be computed tractably from the data.

Suggested Citation

  • Meilă, Marina, 2019. "Good (K-means) clusterings are unique (up to small perturbations)," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 1-17.
    • Handle: RePEc:eee:jmvana:v:173:y:2019:i:c:p:1-17
    DOI: 10.1016/j.jmva.2018.12.008
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    References listed on IDEAS

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    1. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
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