4 research outputs found
Progressive Wasserstein Barycenters of Persistence Diagrams
This paper presents an efficient algorithm for the progressive approximation
of Wasserstein barycenters of persistence diagrams, with applications to the
visual analysis of ensemble data. Given a set of scalar fields, our approach
enables the computation of a persistence diagram which is representative of the
set, and which visually conveys the number, data ranges and saliences of the
main features of interest found in the set. Such representative diagrams are
obtained by computing explicitly the discrete Wasserstein barycenter of the set
of persistence diagrams, a notoriously computationally intensive task. In
particular, we revisit efficient algorithms for Wasserstein distance
approximation [12,51] to extend previous work on barycenter estimation [94]. We
present a new fast algorithm, which progressively approximates the barycenter
by iteratively increasing the computation accuracy as well as the number of
persistent features in the output diagram. Such a progressivity drastically
improves convergence in practice and allows to design an interruptible
algorithm, capable of respecting computation time constraints. This enables the
approximation of Wasserstein barycenters within interactive times. We present
an application to ensemble clustering where we revisit the k-means algorithm to
exploit our barycenters and compute, within execution time constraints,
meaningful clusters of ensemble data along with their barycenter diagram.
Extensive experiments on synthetic and real-life data sets report that our
algorithm converges to barycenters that are qualitatively meaningful with
regard to the applications, and quantitatively comparable to previous
techniques, while offering an order of magnitude speedup when run until
convergence (without time constraint). Our algorithm can be trivially
parallelized to provide additional speedups in practice on standard
workstations. [...