Computational Topology Techniques for Characterizing Time-Series Data

  • Nicole Sanderson
  • Elliott Shugerman
  • Samantha Molnar
  • James D. Meiss
  • Elizabeth Bradley
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10584)

Abstract

Topological data analysis (TDA), while abstract, allows a characterization of time-series data obtained from nonlinear and complex dynamical systems. Though it is surprising that such an abstract measure of structure—counting pieces and holes—could be useful for real-world data, TDA lets us compare different systems, and even do membership testing or change-point detection. However, TDA is computationally expensive and involves a number of free parameters. This complexity can be obviated by coarse-graining, using a construct called the witness complex. The parametric dependence gives rise to the concept of persistent homology: how shape changes with scale. Its results allow us to distinguish time-series data from different systems—e.g., the same note played on different musical instruments.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Nicole Sanderson
    • 1
  • Elliott Shugerman
    • 1
  • Samantha Molnar
    • 1
  • James D. Meiss
    • 1
  • Elizabeth Bradley
    • 1
  1. 1.University of ColoradoBoulderUSA

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