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Strong Consistency of Reduced K-means Clustering

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  • Yoshikazu Terada

Abstract

type="main" xml:id="sjos12074-abs-0001"> Reduced k-means clustering is a method for clustering objects in a low-dimensional subspace. The advantage of this method is that both clustering of objects and low-dimensional subspace reflecting the cluster structure are simultaneously obtained. In this paper, the relationship between conventional k-means clustering and reduced k-means clustering is discussed. Conditions ensuring almost sure convergence of the estimator of reduced k-means clustering as unboundedly increasing sample size have been presented. The results for a more general model considering conventional k-means clustering and reduced k-means clustering are provided in this paper. Moreover, a consistent selection of the numbers of clusters and dimensions is described.

Suggested Citation

  • Yoshikazu Terada, 2014. "Strong Consistency of Reduced K-means Clustering," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 913-931, December.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:4:p:913-931
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    File URL: http://hdl.handle.net/10.1111/sjos.12074
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    References listed on IDEAS

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    1. C. Abraham & P. A. Cornillon & E. Matzner‐Løber & N. Molinari, 2003. "Unsupervised Curve Clustering using B‐Splines," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(3), pages 581-595, September.
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    6. R. C. H. Cheng & W. B. Liu, 2001. "The Consistency of Estimators in Finite Mixture Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(4), pages 603-616, December.
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    Cited by:

    1. Gautier Marti & S'ebastien Andler & Frank Nielsen & Philippe Donnat, 2016. "Clustering Financial Time Series: How Long is Enough?," Papers 1603.04017, arXiv.org, revised Apr 2016.
    2. Gautier Marti & Frank Nielsen & Philippe Donnat & S'ebastien Andler, 2016. "On clustering financial time series: a need for distances between dependent random variables," Papers 1603.07822, arXiv.org.
    3. Yoshikazu Terada, 2015. "Strong consistency of factorial $$K$$ K -means clustering," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(2), pages 335-357, April.
    4. Gautier Marti & Sébastien Andler & Frank Nielsen & Philippe Donnat, 2016. "Clustering Financial Time Series: How Long is Enough?," Post-Print hal-01400395, HAL.
    5. Matteo Barigozzi, 2023. "Quasi Maximum Likelihood Estimation of High-Dimensional Factor Models: A Critical Review," Papers 2303.11777, arXiv.org, revised Dec 2023.
    6. Jiangtao Duan & Wei Gao & Hao Qu & Hon Keung Tony, 2019. "Subspace Clustering for Panel Data with Interactive Effects," Papers 1909.09928, arXiv.org, revised Feb 2021.
    7. 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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