Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kernel Smoothing, Mean Shift, and Their Learning Theory with Directional
  Data   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.

28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th