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Introduction to Persistent Homology

Author Matthew L. Wright



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LIPIcs.SoCG.2016.72.pdf
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Matthew L. Wright

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Matthew L. Wright. Introduction to Persistent Homology. In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, pp. 72:1-72:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.SoCG.2016.72

Abstract

This video presents an introduction to persistent homology, aimed at a viewer who has mathematical aptitude but not necessarily knowledge of algebraic topology. Persistent homology is an algebraic method of discerning the topological features of complex data, which in recent years has found applications in fields such as image processing and biological systems. Using smooth animations, the video conveys the intuition behind persistent homology, while giving a taste of its key properties, applications, and mathematical underpinnings.
Keywords
  • Persistent Homology
  • Topological Data Analysi

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References

  1. P. Bendich, J.S. Marron, E. Miller, A. Pieloch, and S. Skwerer. Persistent homology analysis of brain artery trees. Annals of Applied Statistics, to appear. Google Scholar
  2. G. Carlsson, T. Ishkhanov, V. de Silva, and A. Zomorodian. On the local behavior of spaces of natural images. International Journal of Computer Vision, 76(1):1-12, 2008. Google Scholar
  3. J.M. Chan, G. Carlsson, and R. Rabadan. Topology of viral evolution. Proceedings of the National Academy of Sciences, 110(46), November 2013. Google Scholar
  4. D. Cohen-Steiner, H. Edelsbrunner, and J. Harer. Stability of persistence diagrams. Discrete and Computational Geometry, 37(1):103-120, 2007. Google Scholar
  5. V. de Silva and R. Ghrist. Coverage in sensor networks via persistent homology. Algebraic and Geometric Topology, 7:339-358, 2007. Google Scholar
  6. H. Edelsbrunner and J. Harer. Persistent homology: a survey. In Surveys on discrete and computational geometry: twenty years later: AMS-IMS-SIAM Joint Summer Research Conference, June 18-22, 2006, Snowbird, Utah, volume 453, page 257. American Mathematical Society, 2008. Google Scholar
  7. H. Edelsbrunner, D. Letscher, and A. Zomorodian. Topological persistence and simplification. Discrete and Computational Geometry, 28(4):511-533, 2002. Google Scholar
  8. J. Perea and G. Carlsson. A klein-bottle-based dictionary for texture representation. International Journal of Computer Vision, 107(1):75-97, 2014. Google Scholar
  9. J. Perea, A. Deckard, S.B. Haase, and J. Harer. Sw1pers: Sliding windows and 1-persistence scoring; discovering periodicity in gene expression time series data. BMC Bioinformatics, 16(1), 2015. Google Scholar
  10. K. Turner, S. Mukherjee, and Doug M Boyer. Sufficient statistics for shapes and surfaces. preprint, 2013. Google Scholar
  11. A. Zomorodian and G. Carlsson. Computing persistent homology. Discrete and Computational Geometry, 33(2):249-274, 2005. Google Scholar
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