1 research outputs found
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.Comment: 92 pages, 11 figures. Accepted to the Journal of Machine Learning
Researc