Κ-means clustering on the space of persistence diagrams
Κ-means clustering on the space of persistence diagrams
复制标题
持久性图空间上的 Κ 均值聚类
DOI：
10.1117/12.2273067
复制
发表时间：
2017
期刊：
影响因子：
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通讯作者：
Joshua L. Mike
中科院分区：
文献类型：
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作者：
Andrew Marchese;V. Maroulas;Joshua L. Mike
最近的一组研究旨在将拓扑和几何理论应用于数据分析。然而，需要作出更多努力，将统计思想和结构纳入这些分析方法。为此，我们提出了持久的同源聚类技术，通过数据分析的角度。这些技术提供了深入了解底层动态的结构，并能够识别重要的形状属性，如周期性，混沌和多稳定性。此外，在拓扑数据空间上引入定量结构允许对数据的几何形状的严格理解，这是用于仔细检查固有动态的形态的强大工具。此外，我们说明了这些技术和结果的优势，通过来自动力系统的应用程序的例子。
A recent cohort of research aims to apply topological and geometric theory to data analysis. However, more effort is needed to incorporate statistical ideas and structure to these analysis methods. To this end, we present persistent homology clustering techniques through the perspective of data analysis. These techniques provide insight into the structure of the underlying dynamic and are able to recognize important shape properties such as periodicity, chaos, and multi-stability. Moreover, introducing quantitative structure on the topological data space allows for rigorous understanding of the data's geometry, a powerful tool for scrutinizing the morphology of the inherent dynamic. Additionally, we illustrate the advantages of these techniques and results through examples derived from dynamical systems applications.