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A Topological Approach to Representational Data Models

  • Emilie Purvine
  • Sinan Aksoy
  • Cliff Joslyn
  • Kathleen Nowak
  • Brenda Praggastis
  • Michael Robinson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10904)

Abstract

As data accumulate faster and bigger, building representational models has turned into an art form. Despite sharing common data types, each scientific discipline often takes a different approach. In this work, we propose representational models grounded in the mathematics of algebraic topology to understand foundational data types. We present hypergraphs for multi-relational data, point clouds for vector data, and sheaf models when both data types are present and interrelated. These three models use similar principles from algebraic topology and provide a domain-agnostic framework. We will discuss each method, provide references to their foundational mathematical papers, and give examples of their use.

Keywords

Relational data Vector data Hypergraph models Topological data models Data-agnostic models 

Notes

Acknowledgements

We wish to thank Prof. Francisco Munoz, University of Chile, for providing the sample power grid data studied in Sect. 3.3, and Will Hutton, Pacific Northwest National Laboratory, and his team for providing the data described in Sect. 3.2. This work was supported in part by (a) the Applied Mathematics Program of the Office of Advanced Scientific Computing Research within the Office of Science of the U.S. Department of Energy (DOE) through the Multifaceted Mathematics for Complex Energy Systems (M2ACS) project, (b) the Asymmetric Resilient Cybersecurity Initiative at Pacific Northwest National Laboratory, and (c) the High Performance Data Analytics program at the Pacific Northwest National Laboratory (PNNL). PNNL is operated by Battelle for the United States Department of Energy under Contract DE-AC05-76RL01830.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Emilie Purvine
    • 1
  • Sinan Aksoy
    • 2
  • Cliff Joslyn
    • 1
  • Kathleen Nowak
    • 2
  • Brenda Praggastis
    • 1
  • Michael Robinson
    • 3
  1. 1.Pacific Northwest National LaboratorySeattleUSA
  2. 2.Pacific Northwest National LaboratoryRichlandUSA
  3. 3.American UniversityWashington, DCUSA

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