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Estimation of level set trees using adaptive partitions

Author

Listed:
  • Lasse Holmström

    (University of Oulu)

  • Kyösti Karttunen

    (University of Oulu)

  • Jussi Klemelä

Abstract

We present methods for the estimation of level sets, a level set tree, and a volume function of a multivariate density function. The methods are such that the computation is feasible and estimation is statistically efficient in moderate dimensional cases ( $$d\approx 8$$ d ≈ 8 ) and for moderate sample sizes ( $$n\approx $$ n ≈ 50,000). We apply kernel estimation together with an adaptive partition of the sample space. We illustrate how level set trees can be applied in cluster analysis and in flow cytometry.

Suggested Citation

  • Lasse Holmström & Kyösti Karttunen & Jussi Klemelä, 2017. "Estimation of level set trees using adaptive partitions," Computational Statistics, Springer, vol. 32(3), pages 1139-1163, September.
    • Handle: RePEc:spr:compst:v:32:y:2017:i:3:d:10.1007_s00180-016-0702-2
    DOI: 10.1007/s00180-016-0702-2
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    References listed on IDEAS

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    1. Baíllo, Amparo & Cuesta-Albertos, Juan A. & Cuevas, Antonio, 2001. "Convergence rates in nonparametric estimation of level sets," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 27-35, May.
    2. Cuevas, Antonio & Febrero, Manuel & Fraiman, Ricardo, 2001. "Cluster analysis: a further approach based on density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 36(4), pages 441-459, June.
    3. Nolan, D., 1991. "The excess-mass ellipsoid," Journal of Multivariate Analysis, Elsevier, vol. 39(2), pages 348-371, November.
    4. Cadre, BenoI^t, 2006. "Kernel estimation of density level sets," Journal of Multivariate Analysis, Elsevier, vol. 97(4), pages 999-1023, April.
    5. Burman, Prabir & Polonik, Wolfgang, 2009. "Multivariate mode hunting: Data analytic tools with measures of significance," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1198-1218, July.
    6. Duong, Tarn & Cowling, Arianna & Koch, Inge & Wand, M.P., 2008. "Feature significance for multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4225-4242, May.
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    Cited by:

    1. Vuollo, Ville & Holmström, Lasse, 2018. "A scale space approach for exploring structure in spherical data," Computational Statistics & Data Analysis, Elsevier, vol. 125(C), pages 57-69.

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