15 papers
Fast Approximation of Persistence Diagrams with Guarantees
Jules Vidal, Julien Tierny
This paper presents an algorithm for the efficient approximation of the saddle-extremum persistence diagram of a scalar field. Vidal et al. introduced recently a fast algorithm for…
Wasserstein Distances, Geodesics and Barycenters of Merge Trees
Mathieu Pont, Jules Vidal, Julie Delon +1
This paper presents a unified computational framework for the estimation of distances, geodesics and barycenters of merge trees. We extend recent work on the edit distance [106] an…
TopoMap: A 0-dimensional Homology Preserving Projection of High-Dimensional Data
Harish Doraiswamy, Julien Tierny, Paulo J. S. Silva +2
Multidimensional Projection is a fundamental tool for high-dimensional data analytics and visualization. With very few exceptions, projection techniques are designed to map data fr…
Localized Topological Simplification of Scalar Data
Jonas Lukasczyk, Christoph Garth, Ross Maciejewski +1
This paper describes a localized algorithm for the topological simplification of scalar data, an essential pre-processing step of topological data analysis (TDA). Given a scalar fi…
A Progressive Approach to Scalar Field Topology
Jules Vidal, Pierre Guillou, Julien Tierny
This paper introduces progressive algorithms for the topological analysis of scalar data. Our approach is based on a hierarchical representation of the input data and the fast iden…
Statistical Parameter Selection for Clustering Persistence Diagrams
Max Kontak, Jules Vidal, Julien Tierny
In urgent decision making applications, ensemble simulations are an important way to determine different outcome scenarios based on currently available data. In this paper, we will…