  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.
