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Activity Number:
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103
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Type:
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Contributed
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Date/Time:
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Monday, August 4, 2008 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Nonparametric Statistics
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| Abstract - #301118 |
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Title:
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Analysis of the Shapes of Unimodal Densities with Nonparametric Density Estimation
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Author(s):
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Jussi Klemela*+
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Companies:
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University of Oulu
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Address:
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Department of Mathematical Sciences, Oulun Yliopisto, International, 90014, Finland
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Keywords:
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multivariate data ; nonparametric density estimation ; level set trees ; shape analysis ; visualization of multivariate functions
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Abstract:
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Nonparametric density estimation has been applied successfully in mode detection. However, nonparametric analysis of the shapes of unimodal densities has attracted less interest. Level set tree based techniques can be applied to analyze the shapes of unimodal densities. A level set tree of a function is a tree structure of the separated components of level sets of the function. Level set trees can be used to describe not only the shapes of functions but also the shapes of multidimensional sets; we can define a distance function or a height function on a set and construct a level set tree of this function. Finally, level set trees can be used to describe the shapes of point clouds, by applying appropriate smoothing. This leads to a computationally efficient way of describing the shapes of unimodal densities.
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