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arXiv · 1708.09359

Computational Topology Techniques for Characterizing Time-Series Data

Nicole Sanderson·Elliott Shugerman·Samantha Molnar·James D. Meiss·Elizabeth Bradley
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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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Nicole Sanderson, Elliott Shugerman, Samantha Molnar, James D. Meiss, Elizabeth Bradley. 2018-10-12. Computational Topology Techniques for Characterizing Time-Series Data. https://doi.org/10.1007/978-3-319-68765-0_24

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