Academics > (ДВ3) Topological Data Analysis (sa)

(ДВ3) Topological Data Analysis (sa)

Тип: На вибір студента

Кафедра: mathematical modeling of social and economics processes

Навчальний план

СеместрКредитиЗвітність
65Залік

Лекції

СеместрК-сть годинЛекторГрупа(и)
632O. Yu. LysetskaPMa-32

Лабораторні

СеместрК-сть годинГрупаВикладач(і)
632PMa-32

Опис курсу

Topological Data Analysis (TDA) is a modern data science field, where tools of the topological algebra for the detection of persistent structural features in the complex, noized or/and heighdimentional data are used. This course gives the basic understanding about the general topology, algebraic topology, main concepts and algorithms of the TDA (persistant homologies, symplicial complex, MAPPER, persistence, etc.). The TDA course as well provides practical development of the main TDA techniques  in the clusterization, anomaly detection, and shape analysis tasks.

Рекомендована література

Main sources

 

  1. Edelsbrunner, H., & Harer, J. (2010). Computational topology: An introduction. American Mathematical Society.
  2. Carlsson, G., & Vejdemo-Johansson, M. (2021). Topological data analysis with applications. Cambridge University Press. https://doi.org/10.1017/9781108975704
  3. Dey, T. K., & Wang, Y. (2022). Computational topology for data analysis. Cambridge University Press. https://doi.org/10.1017/9781009098168
  4. Ghrist R., Barcodes: The persistent topology of data. American Mathematical Society (2007).
  5. Munch, E. (2017). A user’s guide to topological data analysis. Journal of Learning Analytics, 4(2), 47–61. https://doi.org/10.18608/jla.2017.42.6
  6. giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration, Tauzin et al, arXiv:2004.02551, 2020.
  7. Scikit-TDA, Topological Data Analysis for the Python ecosystem. http://scikit-tda.org
  8. The Topology ToolKit (TTK), https://topology-tool-kit.github.io/
  9. The GUDHI (Geometry Understanding in Higher Dimensions) library for Topological Data Analysis (TDA), https://gudhi.inria.fr/

 

Additional sources

 

  1. Carlsson, G. (2009). Topology and data. Bulletin of the American Mathematical Society, 46(2), 255–308. https://doi.org/10.1090/S0273-0979-09-01249-X
  2. Maria, C., Boissonnat, J.-D., Glisse, M., & Yvinec, M. (2014). The Gudhi library: Simplicial complexes and persistent homology. In H. Hong & C. Yap (Eds.), Mathematical Software – ICMS 2014 (pp. 167–174). Springer. https://doi.org/10.1007/978-3-662-44199-2_28
  3. Bauer, U. (2019). Ripser: efficient computation of Vietoris–Rips persistence barcodes. Journal of Open Source Software, 4(41), 1691. https://doi.org/10.21105/joss.01691
  4. Rabadán, R., & Blumberg, A. J. (2019). Topological data analysis for genomics and evolution: Topology in biology. Cambridge University Press. https://doi.org/10.1017/9781316671665
  5. Oudot, S. Y. (2015). Persistence theory: From quiver representations to data analysis. American Mathematical Society. https://doi.org/10.1090/surv/209