A Stable Cardinality Distance for Topological Classification
This work addresses classification challenges in materials science with noisy data, but it is incremental as it builds on existing topological methods.
The authors tackled the problem of classifying point cloud data from materials science by introducing a new stable distance metric for persistence diagrams, which successfully determined crystal structures on noisy and sparse synthetic atom probe tomography data.
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.