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Clustering and visualizing high-dimensional (HD) data are important tasks ina variety of fields. For example, in bioinformatics, they are crucial foranalyses of single-cell data such as mass cytometry (CyTOF) data. Some of themost effective algorithms for clustering HD data are based on representing thedata by nodes in a graph, with edges connecting neighbouring nodes according tosome measure of similarity or distance. However, users of graph-basedalgorithms are typically faced with the critical but challenging task ofchoosing the value of an input parameter that sets the size of neighbourhoodsin the graph, e.g. the number of nearest neighbours to which to connect eachnode or a threshold distance for connecting nodes. The burden on the user couldbe alleviated by a measure of inter-node similarity that can have value 0 fordissimilar nodes without requiring any user-defined parameters or thresholds.This would determine the neighbourhoods automatically while still yielding asparse graph. To this end, I propose a new method called ASTRICS to measuresimilarity between clusters of HD data points based on local dimensionalityreduction and triangulation of critical alpha shapes. I show that my ASTRICSsimilarity measure can facilitate both clustering and visualization of HD databy using it in Stage 2 of a three-stage pipeline: Stage 1 = perform an initialclustering of the data by any method; Stage 2 = let graph nodes representinitial clusters instead of individual data points and use ASTRICS toautomatically define edges between nodes; Stage 3 = use the graph for furtherclustering and visualization. This trades the critical task of choosing a graphneighbourhood size for the easier task of essentially choosing a resolution atwhich to view the data. The graph and consequently downstream clustering andvisualization are then automatically adapted to the chosen resolution.

Measuring inter-cluster similarities with Alpha Shape TRIangulation in  loCal Subspaces (ASTRICS) facilitates visualization and clustering of  high-dimensional data