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Advances in Data Analysis and Classification

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27-11-2019 | Regular Article

A stable cardinality distance for topological classification

Authors: Vasileios Maroulas, Cassie Putman Micucci, Adam Spannaus

Published in: Advances in Data Analysis and Classification | Issue 3/2020

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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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Title: A stable cardinality distance for topological classification
Authors: Vasileios Maroulas
Cassie Putman Micucci
Adam Spannaus
Publication date: 27-11-2019
Publisher: Springer Berlin Heidelberg
Published in: Advances in Data Analysis and Classification / Issue 3/2020
Print ISSN: 1862-5347
Electronic ISSN: 1862-5355
DOI: https://doi.org/10.1007/s11634-019-00378-3

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