数据分析中的持续交互拓学
Jian Liu1, Dong Chen2, Guo-Wei Wei2,3,4
1Mathematical Science Research Center, Chongqing University of Technology, Chongqing 400054, China.
概括
我们介绍了持久相互作用同质学和拉普拉斯语,以通过专注于单个元素来分析复杂系统. 这些新的拓数据分析方法提高了对交互数据的理解,在分子科学中有应用.
科学领域:
- 数学 数学 是一个数学.
- 数据科学数据科学数据科学
- 计算拓学的计算拓学
背景情况:
- 拓数据分析 (TDA) 使用持久的同质性和拉普拉西亚语来从数据中提取特征.
- 传统的方法,如简化复合体,缺乏对复杂系统中单个元素的局部描述.
- 现有的TDA技术与异质互动数据作斗争,并强调特定的系统组件.
研究的目的:
- 引入持久相互作用同类学和持久相互作用拉普拉西安用于局部拓分析.
- 开发方法来强调复杂系统中的单个相互作用元素.
- 扩展TDA以更好地分析交互式数据集和特定数据点.
主要方法:
- 开发了持久相互作用同质性和持久相互作用拉普拉西亚语.
- 证明了作为一个持久模块的持久相互作用同质的稳定性.
- 为离散点集构建了持久相互作用的Vietoris-Rips复合体.
- 这些复合体的计算相互作用同质学和相互作用拉普拉西安.
主要成果:
- 新的方法为单个元素提供了局部化的拓描述.
- 持续的相互作用同质性被证明是一个稳定的持续模块.
- 该框架适用于Euclidean空间中的有限离散点集.
- 在分析分子数据方面证明有用.
结论:
- 持久交互同学学和拉普拉斯学为分析复杂的交互数据提供了强大的工具.
- 这些方法可以将重点放在单个元素上,克服经典TDA的局限性.
- 这种方法对数据科学应用有很大的前景,特别是在化学和材料科学领域.
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