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null (Ed.)In this paper, we propose a new clustering method inspired by mode-clustering that not only finds clusters, but also assigns each cluster with an attribute label. Clusters obtained from our method show connectivity of the underlying distribution. We also design a local two-sample test based on the clustering result that has more power than a conventional method. We apply our method to the Astronomy and GvHD data and show that our method finds meaningful clusters. We also derive the statistical and computational theory of our method.more » « less
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null (Ed.)Directional data consist of observations distributed on a (hyper)sphere, and appear in many applied fields, such as astronomy, ecology, and environmental science. This paper studies both statistical and computational problems of kernel smoothing for directional data. We generalize the classical mean shift algorithm to directional data, which allows us to identify local modes of the directional kernel density estimator (KDE). The statistical convergence rates of the directional KDE and its derivatives are derived, and the problem of mode estimation is examined. We also prove the ascending property of the directional mean shift algorithm and investigate a general problem of gradient ascent on the unit hypersphere. To demonstrate the applicability of the algorithm, we evaluate it as a mode clustering method on both simulated and real-world data sets.more » « less
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