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A stable cardinality distance for topological classification
Advances in Data Analysis and Classification ( IF 1.6 ) Pub Date : 2019-11-27 , DOI: 10.1007/s11634-019-00378-3 Vasileios Maroulas , Cassie Putman Micucci , Adam Spannaus
Advances in Data Analysis and Classification ( IF 1.6 ) Pub Date : 2019-11-27 , DOI: 10.1007/s11634-019-00378-3 Vasileios Maroulas , Cassie Putman Micucci , Adam Spannaus
This work incorporates topological features via persistence diagrams to classify point cloud data arising from materials science. Persistence diagrams are multisets summarizing the connectedness and holes of given data. A new distance on the space of persistence diagrams generates relevant input features for a classification algorithm for materials science data. This distance measures the similarity of persistence diagrams using the cost of matching points and a regularization term corresponding to cardinality differences between diagrams. Establishing stability properties of this distance provides theoretical justification for the use of the distance in comparisons of such diagrams. The classification scheme succeeds in determining the crystal structure of materials on noisy and sparse data retrieved from synthetic atom probe tomography experiments.
中文翻译:
用于拓扑分类的稳定基数距离
这项工作通过持久性图合并了拓扑特征,以对由材料科学产生的点云数据进行分类。持久性图是多集,总结了给定数据的连通性和漏洞。余辉图空间上的新距离为材料科学数据的分类算法生成了相关的输入特征。该距离使用匹配点的成本和对应于图之间基数差异的正则项来度量持久图的相似性。建立此距离的稳定性,可以为此类图的比较提供使用该距离的理论依据。
更新日期:2019-11-27
中文翻译:
用于拓扑分类的稳定基数距离
这项工作通过持久性图合并了拓扑特征,以对由材料科学产生的点云数据进行分类。持久性图是多集,总结了给定数据的连通性和漏洞。余辉图空间上的新距离为材料科学数据的分类算法生成了相关的输入特征。该距离使用匹配点的成本和对应于图之间基数差异的正则项来度量持久图的相似性。建立此距离的稳定性,可以为此类图的比较提供使用该距离的理论依据。