论文标题
球形主曲线
Spherical Principal Curves
论文作者
论文摘要
本文提出了一种新的方法，以减少在球体中观察到的数据。最近开发了几种降低维度的技术，用于分析非欧几里得数据。作为先驱工作，Hauberg（2016）试图对Riemannian流形实施主要曲线。但是，这种方法使用近似值来处理Riemannian流形的数据，这会导致结果扭曲。在这项研究中，我们提出了一种新方法，通过在连续曲线上的数据投影在球体上构建主要曲线。我们的方法在于Hastie and Stuetzle（1989）提出了欧几里得太空数据的主要曲线。我们进一步研究了满足球体上自矛盾的拟议主曲线的平稳性。带有地震数据和仿真示例的真实数据分析的结果证明了该方法的有希望的经验特性。
This paper presents a new approach for dimension reduction of data observed in a sphere. Several dimension reduction techniques have recently developed for the analysis of non-Euclidean data. As a pioneer work, Hauberg (2016) attempted to implement principal curves on Riemannian manifolds. However, this approach uses approximations to deal with data on Riemannian manifolds, which causes distorted results. In this study, we propose a new approach to construct principal curves on a sphere by a projection of the data onto a continuous curve. Our approach lies in the same line of Hastie and Stuetzle (1989) that proposed principal curves for Euclidean space data. We further investigate the stationarity of the proposed principal curves that satisfy the self-consistency on a sphere. Results from real data analysis with earthquake data and simulation examples demonstrate the promising empirical properties of the proposed approach.
