论文标题
内核平滑，平均转移及其学习理论的方向数据
Kernel Smoothing, Mean Shift, and Their Learning Theory with Directional Data
论文作者
论文摘要
方向数据由分布在（超级）球体上的观测值组成，并出现在许多应用领域，例如天文学，生态学和环境科学。本文研究了方向数据的内核平滑的统计和计算问题。我们将经典的平均移位算法推广到方向数据，这使我们能够识别定向内核密度估计器（KDE）的局部模式。定向KDE及其导数的统计收敛速率被得出，并检查了模式估计问题。我们还证明了定向平均移位算法的上升特性，并研究了单位孔洞上梯度上升的一般问题。为了证明该算法的适用性，我们将其评估为模式聚类方法，同时又是模拟和现实世界数据集。
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.
