一个瓦瑟斯坦类型的距离,用于向量束上的高斯混合物,并用于形状分析
Michael Wilson1, Tom Needham2, Chiwoo Park3
1Department of Statistics, Florida State University, Tallahassee, FL 32306 USA.
概括
这项研究引入了一种使用高斯混合模型在几何空间上比较人口的新方法. 该方法可以在纳米粒子制造工艺等应用中进行可靠的变化点检测.
科学领域:
- 计算几何学计算几何学
- 几何统计数据的几何统计
- 对多元组的数据分析.
背景情况:
- 在复杂的几何空间上比较人口,比如里曼的多元体是具有挑战性的.
- 现有的方法经常与这些空间的内在几何学斗争.
- 将种群表示为概率分布是一种常见的方法.
研究的目的:
- 开发一个新的框架来比较居住在有限维可平行化的里曼的多元体和微不足道的向量束上的人口.
- 调整统计方法来分析人口数据与复杂的几何结构.
- 为了能够在几何上下文中对形状数据和时间序列数据进行可靠的分析.
主要方法:
- 在向量捆上将种群表示为高斯混合物,利用碎性.
- 采用基于模式的集群算法进行参数估计.
- 导出一种适合多元体几何学的瓦瑟斯坦类型的度量,用于比较分布.
- 在多种领域建立高斯混合物的识别结果.
- 根据新标准,对高斯混合物进行最佳合的描述.
主要成果:
- 一个新的瓦瑟斯坦类型的度量是衍生出来的,它解释了多重几何.
- 在多种领域证明了高斯混合物的识别结果.
- 该框架在各种几何领域进行了演示,包括预制空间.
- 该方法成功地在制造过程中的纳米粒子形状数据上执行变化点检测.
结论:
- 拟议的框架提供了一个强大而适应性的工具,用于比较几何多元体上的人口.
- 衍生出来的瓦斯斯坦式度量和相关方法增强了几何空间中的统计分析.
- 对纳米粒子制造的应用证明了在工艺监测和质量控制中的实际实用性.
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