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Algorithms for manipulation of level sets of nonparametric density estimates

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Summary

We present algorithms for finding the level set tree of a multivariate density estimate. That is, we find the separated components of level sets of the estimate for a series of levels, gather information on the separated components, such as volume and barycenter, and present the information together with the tree structure of the separated components. The algorithm proceeds by first building a binary tree which partitions the support of the density estimate, followed by bottom-up travels of this tree during which we join those parts of the level sets which touch each other. As a byproduct we present an algorithm for evaluating a kernel estimate on a large multidimensional grid. Since we find the barycenters of the separated components of the level sets also for high levels, our method finds the locations of local extremes of the estimate.

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Authors and Affiliations

  1. Department of Statistics, University of Mannheim, L 7 3–5, Verfügungsgebäude, 68131, Mannheim, Germany

    Jussi Klemelä

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  1. Jussi Klemelä
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Additional information

Writing of this article was financed by Deutsche Forschungsgemeinschaft under project MA1026/8-1.

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Klemelä, J. Algorithms for manipulation of level sets of nonparametric density estimates. Computational Statistics 20, 349–368 (2005). https://doi.org/10.1007/BF02789708

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  • DOI: https://doi.org/10.1007/BF02789708

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