  The tasks of identifying separation structures and clusters in flow data are
fundamental to flow visualization. Significant work has been devoted to these
tasks in flow represented by vector fields, but there are unique challenges in
addressing these tasks for time-varying particle data. The unstructured nature
of particle data, nonuniform and sparse sampling, and the inability to access
arbitrary particles in space-time make it difficult to define separation and
clustering for particle data. We observe that weaker notions of separation and
clustering through continuous measures of these structures are meaningful when
coupled with user exploration. We achieve this goal by defining a measure of
particle similarity between pairs of particles. More specifically, separation
occurs when spatially-localized particles are dissimilar, while clustering is
characterized by sets of particles that are similar to one another. To be
robust to imperfections in sampling we use diffusion geometry to compute
particle similarity. Diffusion geometry is parameterized by a scale that allows
a user to explore separation and clustering in a continuous manner. We
illustrate the benefits of our technique on a variety of 2D and 3D flow
datasets, from particles integrated in fluid simulations based on time-varying
vector fields, to particle-based simulations in astrophysics.
