A stable cardinality distance for topological classification
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 fea...
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| Veröffentlicht in: | Advances in data analysis and classification 2020-09, Vol.14 (3), p.611-628 |
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| container_title | Advances in data analysis and classification |
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| creator | Maroulas, Vasileios Micucci, Cassie Putman Spannaus, Adam |
| description | 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. |
| doi_str_mv | 10.1007/s11634-019-00378-3 |
| format | Article |
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| language | eng |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Algorithms Chemistry and Earth Sciences Classification Computer Science Crystal structure Data Mining and Knowledge Discovery Distance measurement Economics Finance Health Sciences Humanities Insurance Law Management Materials science Mathematics and Statistics Medicine Physics Regular Article Regularization Statistical Theory and Methods Statistics Statistics for Business Statistics for Engineering Statistics for Life Sciences Statistics for Social Sciences Topology |
| title | A stable cardinality distance for topological classification |
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