  Clustering and visualizing high-dimensional (HD) data are important tasks in
a variety of fields. For example, in bioinformatics, they are crucial for
analyses of single-cell data such as mass cytometry (CyTOF) data. Some of the
most effective algorithms for clustering HD data are based on representing the
data by nodes in a graph, with edges connecting neighbouring nodes according to
some measure of similarity or distance. However, users of graph-based
algorithms are typically faced with the critical but challenging task of
choosing the value of an input parameter that sets the size of neighbourhoods
in the graph, e.g. the number of nearest neighbours to which to connect each
node or a threshold distance for connecting nodes. The burden on the user could
be alleviated by a measure of inter-node similarity that can have value 0 for
dissimilar nodes without requiring any user-defined parameters or thresholds.
This would determine the neighbourhoods automatically while still yielding a
sparse graph. To this end, I propose a new method called ASTRICS to measure
similarity between clusters of HD data points based on local dimensionality
reduction and triangulation of critical alpha shapes. I show that my ASTRICS
similarity measure can facilitate both clustering and visualization of HD data
by using it in Stage 2 of a three-stage pipeline: Stage 1 = perform an initial
clustering of the data by any method; Stage 2 = let graph nodes represent
initial clusters instead of individual data points and use ASTRICS to
automatically define edges between nodes; Stage 3 = use the graph for further
clustering and visualization. This trades the critical task of choosing a graph
neighbourhood size for the easier task of essentially choosing a resolution at
which to view the data. The graph and consequently downstream clustering and
visualization are then automatically adapted to the chosen resolution.
