论文标题
一种简单的几何方法，用于导航质心伏罗尼核的能源景观
A simple geometric method for navigating the energy landscape of centroidal Voronoi tessellations
论文作者
论文摘要
在2D域中找到最佳（或低能）质心伏罗尼胶镶嵌（CVT）是一个挑战性的问题。必须浏览一个能量景观，其理想的临界点具有足够小的景点，使它们无法与蒙特卡罗初始化梯度下降方法无法接近。我们提出了一种简单的确定性方法，用于有效地导航能量景观，以便它访问这些低能CVT。该方法具有两个参数，并且基于每个发生器从最近的邻居移开一定距离。我们对这种混合方法的性能进行了统计分析，该分析与劳埃德方法和最先进的Quasi-Newton方法的大量运行结果进行了比较。还考虑了随机替代方案。
Finding optimal (or low energy) centroidal Voronoi tessellations (CVTs) on a 2D domain is a challenging problem. One must navigate an energy landscape whose desirable critical points have sufficiently small basins of attractions that they are inaccessible with Monte-Carlo initialized gradient descent methods. We present a simple deterministic method for efficiently navigating the energy landscape in order to it access these low energy CVTs. The method has two parameters and is based upon each generator moving away from the closest neighbor by a certain distance. We give a statistical analysis of the performance of this hybrid method comparing with the results of a large number of runs for both Lloyd's method and state of the art quasi-Newton methods. Stochastic alternatives are also considered.
