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Activity Number:
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289
- Recent Advances in Mathematical Statistics and Probability
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Type:
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Contributed
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Date/Time:
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Wednesday, August 11, 2021 : 1:30 PM to 3:20 PM
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Sponsor:
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IMS
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Abstract #317981
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Title:
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Kernel Smoothing, Mean Shift, and Their Learning Theory with Directional Data
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Author(s):
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Yikun Zhang* and Yen-Chi Chen
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Companies:
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University of Washington, Seattle and University of Washington
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Keywords:
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Directional data;
Mean shift algorithm;
Kernel smoothing;
mode clustering;
optimization on a manifold
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Abstract:
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Directional data consist of observations distributed on a hypersphere, and appear in many applied fields, such as astronomy, ecology, and environmental science. We discuss both statistical and computational problems of kernel smoothing for directional data. We derive the statistical convergence rates of directional KDE and its derivatives and examine the problem of mode estimation. Given that the classical mean shift algorithm can be generalized to directional data, we also study the algorithmic convergence rate of the directional mean shift algorithm by viewing it as a gradient ascent method on the unit hypersphere. To demonstrate the applicability of our proposed algorithm, we evaluate it as a mode clustering method on both simulated and real-world datasets.
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Authors who are presenting talks have a * after their name.
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