A stable cardinality distance for topological classification

Vasileios Maroulas; Cassie Putman Micucci; Adam Spannaus

doi:10.1007/s11634-019-00378-3

A stable cardinality distance for topological classification

Vasileios Maroulas, Cassie Putman Micucci, Adam Spannaus

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	611-628
Number of pages	18
Journal	Advances in Data Analysis and Classification
Volume	14
Issue number	3
DOIs	https://doi.org/10.1007/s11634-019-00378-3
State	Published - Sep 1 2020
Externally published	Yes

Funding

The authors would like to thank the anonymous associate editor and two anonymous reviewers for their insightful comments which substantially improved the manuscript. Moreover, the authors would like to thank Professor David J. Keffer (Department of Materials Science and Engineering at The University of Tennessee) for providing the codes which create the realistic APT datasets and for useful discussions, as well as Professor Kody J.H. Law (School of Mathematics at the University of Manchester) for insightful discussions. This work has been partially supported by the ARO Grant # W911NF-17-1-0313, the NSF DMS-1821241, and UTK 2019 Research Seed Funding-Interdisciplinary.

Funders	Funder number
National Science Foundation	DMS-1821241
Directorate for Mathematical and Physical Sciences	1821241
Army Research Office	W911NF-17-1-0313
University of Tennessee
University of Manchester

Keywords

Classification
Crystal structure of materials
Persistence diagrams
Persistent homology
Stability

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10.1007/s11634-019-00378-3

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abstract = "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.",

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KW - Crystal structure of materials

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KW - Persistent homology

KW - Stability

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A stable cardinality distance for topological classification

Abstract

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Keywords

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