当前位置: X-MOL 学术Comput. Chem. Eng. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
The Euler characteristic: A general topological descriptor for complex data
Computers & Chemical Engineering ( IF 4.3 ) Pub Date : 2021-08-02 , DOI: 10.1016/j.compchemeng.2021.107463
Alexander Smith 1 , Victor M. Zavala 1
Affiliation  

Datasets are mathematical objects (e.g., point clouds, matrices, graphs, images, fields/functions) that have shape. This shape encodes important knowledge about the system under study. Topology is an area of mathematics that provides diverse tools to characterize the shape of data objects. In this work, we study a specific tool known as the Euler characteristic (EC). The EC is a general, low-dimensional, and interpretable descriptor of topological spaces defined by data objects. We revise the mathematical foundations of the EC and highlight its connections with statistics, linear algebra, field theory, and graph theory. We discuss advantages offered by the use of the EC in the characterization of complex datasets; to do so, we illustrate its use in different applications of interest in chemical engineering such as process monitoring, flow cytometry, and microscopy. We show that the EC provides a descriptor that effectively reduces complex datasets and that this reduction facilitates tasks such as visualization, regression, classification, and clustering.



中文翻译:

欧拉特征:复杂数据的一般拓扑描述符

数据集是具有形状的数学对象(例如,点云、矩阵、图形、图像、字段/函数)。这种形状编码了有关所研究系统的重要知识。拓扑是数学的一个领域,它提供了多种工具来表征数据对象的形状。在这项工作中,我们研究了一种称为欧拉特性 (EC) 的特定工具。EC 是由数据对象定义的拓扑空间的通用、低维和可解释的描述符。我们修改了 EC 的数学基础,并强调了它与统计学、线性代数、场论和图论的联系。我们讨论了在复杂数据集表征中使用 EC 所提供的优势;为此,我们说明了它在化学工程中感兴趣的不同应用中的使用,例如过程监控,流式细胞术和显微镜。我们表明 EC 提供了一个描述符,可以有效地减少复杂的数据集,并且这种减少有利于可视化、回归、分类和聚类等任务。

更新日期:2021-08-15
down
wechat
bug