May 19 – 24 , 2019, Dagstuhl Seminar 19212

Topology, Computation and Data Analysis


Michael Kerber (TU Graz, AT)
Vijay Natarajan (Indian Institute of Science – Bangalore, IN)
Bei Wang (University of Utah – Salt Lake City, US)

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Annette Beyer for administrative matters

Shida Kunz for scientific matters


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Topology is the study of connectivity of space that abstracts away geometry and provides succinct representations of the space and functions defined on it. Topology-based methods for data analysis have received considerable attention in the recent years given its promise to handle large and feature-rich data that are becoming increasingly common. Computing topological properties in the data domain and/or range is a step in the direction of more abstract, higher-level data analysis and visualization. Such an approach has become more important in the context of automatic and semi-automatic data exploration, analysis, and understanding. The primary attraction for topology-based methods is the ability to generate summary qualitative views of large data sets. Such views often require fewer geometrical primitives to be extracted, stored, and to be visualized as compared to views obtained directly from the raw data.

Two communities, computational topology and topological visualization, have made significant progress during the past two decades on developing topological abstractions and applying them to data analysis. In addition, there are multiple other research programs (relatively fewer in number) on this topic within the statistics and machine learning fields, and within a few application domains. Computational topology grew from within computational geometry and algebraic topology and studies algorithmic questions on topological structures. The focus of topological data analysis and topological visualization is data – algorithms, methods, and systems for improved and intuitive understanding of data via application of topological structures. Researchers in computational topology typically have a math or theoretical computer science background whereas visualization researchers have a computational, computer engineering, or applied background. There is very little communication between the two communities due to the different origins and the fact that there are no common conferences or symposia where they come together.

The goal of this Dagstuhl Seminar is to strengthen existing ties, establish new ones, identify challenges that requires the two communities to work together, and establish mechanisms for increased communication and transfer of results from one to the other. The benefits of the inter-community ties are already well appreciated, e.g., by the participants of the Dagstuhl Seminar “Topology, Computation and Data Analysis” (17292) in July 2017, which had a similar but not identical focus.

We have chosen four current and emerging topics that will benefit from an inter-community discussion: (a) Reeb graphs, Reeb Spaces, and Mappers; (b) topological analysis and visualization of multivariate data; (c) new opportunities for vector field topology; and (d) software tools and libraries. These topics are common to both communities, with different aspects studied within each community. This will help both build the ties and identify new approaches to future research challenges. Among the invitees are the leading experts on these topics in each community: the concentration of expertise is also intended to provide opportunities to define a longer-term and larger-scale roadmap for research into computational applications of topology to data analysis at all scales.

  Creative Commons BY 3.0 DE
  Michael Kerber, Vijay Natarajan, and Bei Wang

Related Dagstuhl Seminar


  • Data Structures / Algorithms / Complexity


  • Computational topology
  • Topological data analysis

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