A stable cardinality distance for topological classification

Vasileios Maroulas (), Cassie Putman Micucci () and Adam Spannaus ()
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Vasileios Maroulas: University of Tennessee
Cassie Putman Micucci: University of Tennessee
Adam Spannaus: University of Tennessee

Advances in Data Analysis and Classification, 2020, vol. 14, issue 3, No 6, 628 pages

Abstract: 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.

Keywords: Stability; Classification; Persistent homology; Persistence diagrams; Crystal structure of materials; 62H30; 62P30; 55N99; 54H99 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s11634-019-00378-3

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