A Simple Geometric Method For Navigating The Energy Landscape Of Centroidal Voronoi Tessellations

SIAM JOURNAL ON SCIENTIFIC COMPUTING(2021)

引用 4|浏览2
暂无评分
摘要
Finding optimal (or low energy) centroidal Voronoi tessellations (CVTs) on a two-dimensional domain is a challenging problem. One must navigate an energy landscape whose desirable critical points have sufficiently small basins of attractions that are inaccessible with Monte Carlo initialized gradient descent methods. We present a simple deterministic method for efficiently navigating the energy landscape in order to 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.
更多
查看译文
关键词
centroidal Voronoi tessellation, global optimization, energy ground state, optimal vector quantizer, regularity measures
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要