对于良好的格子点套件的一些改进
Yu-Xuan Lin1,2, Tian-Yu Yan3, Kai-Tai Fang2,4
1Research Center for Frontier Fundamental Studies, Zhejiang Lab, Kechuang Avenue, Zhongtai Sub-District, Yuhang District, Hangzhou 311121, China.
Entropy (Basel, Switzerland)
|November 27, 2024
概括
通用好的格子点 (GGLP) 集,通过线性级别排列,从好的格子点 (GLP) 集衍生,增强填充空间的特性. 这些改进的GLP集在计算机实验等应用中表现出卓越的性能.
科学领域:
- 数学理论是数的理论.
- 应用数学 应用数学 应用数学
- 计算统计的计算统计.
背景情况:
- 良好的格子点 (GLP) 集是数字理论方法,以其填充空间的特性而受到重视.
- 增强GLP集对于需要更好的分布的应用程序至关重要,特别是对于大型数据集.
- 现有的GLP套件被广泛使用,但在空间填充能力方面有改进的余地.
研究的目的:
- 引入和评估通用良好格子点 (GGLP) 集.
- 评估线性级别排列对GLP集合属性的影响.
- 通过使用新的施工方法,提高GLP套件的填充空间特性.
主要方法:
- 使用Kullback-Leibler (KL) 差异来测量GLP和GLP集合分布.
- 对GLP集进行了线性级别的变换,以创建GLP集.
- 采用接受值的算法和弗罗贝尼乌斯距离来构建和评估大型GLP集.
主要成果:
- 通过线性级别排列创建的GGLP集不会减少最大距离标准.
- 与最初的GLP集相比,GLLP集显示了增强的填充空间特性.
- KL差异分析表明GGLP集保持分布相似性,特别是在大型数据集中.
结论:
- 与传统的GLP套件相比,GLP套件提供了更好的填充空间特性.
- 构建方法,包括接受值的算法,对于生成优越的网格点集是有效的.
- GGLP集在计算机实验和选择代表点等应用中展示了实际优势.
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