Alpha-X: An Alpha Shape-based Hierarchical Clustering Algorithm

Alpha-X is an ongoing exploration into the utility of alpha shapes in describing hierarchical clustering. Based on the Delaunay triangulation of a set of points, alpha shapes describe concrete boundaries of regions around point clusters that are associated at distances less than some characteristic length scale a. The concept of alpha shapes is a discrete approach and can thus be applied to sets of positions of stars to evaluate stellar clustering. We are developing a representation of point-cloud substructures as a values in tree representations which capture the hierarchical lineage of structure at different values of a. With this approach, alpha shapes could be used in an new hierarchical cluster detection and characterization method that naturally defines boundaries associated with identified clusters.