Topology

From Ioannis Kourouklides
Jump to navigation Jump to search

This page contains resources about Geometric Topology and Topology in general, including Topological Data Analysis and Computational Topology

Subfields and Concepts

  • Metric Geometry 
    • Metric / Distance function
    • Geodesics
  • Topological Groups
    • Pontryagin duality (in Harmonic Analysis)
    • Locally Compact Abelian Group (LCA Group or LCAG)
  • Topological Spaces
    • Manifold
      • Riemannian Manifolds
    • Metric space
      • Riemannian metric
      • Fisher information metric / Fisher–Rao metric
  • Computational Topology / Algorithmic Topology
    • Algorithmic 3-manifold Theory
    • Algorithmic Knot Theory
    • Computational homotopy
    • Computational homology
  • Topological Data Analysis
    • barcode / persistence diagram
    • persistent homology / topological persistence

Online Courses

Video Lectures


Lecture Notes

Books

  • Boissonnat, J. D., Chazal, F., & Yvinec, M. (2018). Geometric and Topological Inference. Cambridge University Press. (link)
  • Tierny, J. (2018). Introduction to topological data analysis. UPMC, LIP6. (link)
  • Oudot, S. Y. (2015). Persistence Theory: From Quiver Representations to Data Analysis . American Mathematical Society.
  • Ghrist, R. W. (2014). Elementary applied topology. Createspace. (link)
  • Edelsbrunner, H., & Harer, J. (2010). Computational Topology: An Introduction. American Mathematical Society. (link)
  • Hatcher, A. (2002). Algebraic Topology. Cambridge University Press. (link)

Scholarly Articles

  • Carriere, M., Michel, B., & Oudot, S. (2018). Statistical analysis and parameter selection for Mapper. Journal of Machine Learning Research, 19(1), 478-516.
  • Wasserman, L. (2018). Topological data analysis. Annual Review of Statistics and Its Application, 5, 501-532.
  • Chazal, F., & Michel, B. (2017). An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists. arXiv preprint arXiv:1710.04019.
  • Chazal, F., Fasy, B., Lecci, F., Michel, B., Rinaldo, A., Rinaldo, A., & Wasserman, L. (2017). Robust topological inference: Distance to a measure and kernel distance. Journal of Machine Learning Research, 18(1), 5845-5884.
  • Hofer, C., Kwitt, R., Niethammer, M., & Uhl, A. (2017). Deep learning with topological signatures. In Advances in Neural Information Processing Systems (pp. 1634-1644).
  • Adams, H., Emerson, T., Kirby, M., Neville, R., Peterson, C., Shipman, P., ... & Ziegelmeier, L. (2017). Persistence images: A stable vector representation of persistent homology. Journal of Machine Learning Research, 18(1), 218-252.
  • Seversky, L. M., Davis, S., & Berger, M. (2016). On time-series topological data analysis: New data and opportunities. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (pp. 59-67).
  • Kusano, G., Hiraoka, Y., & Fukumizu, K. (2016). Persistence weighted Gaussian kernel for topological data analysis. In Proceedings of the 33rd International Conference on Machine Learning (pp. 2004-2013).
  • Chazal, F., Fasy, B. T., Lecci, F., Michel, B., Rinaldo, A., & Wasserman, L. (2015). Subsampling methods for persistent homology. In Proceedings of the 32nd International Conference on Machine Learning (pp. 2143-2151).
  • Chazal, F., Glisse, M., Labruere, C., & Michel, B. (2015). Convergence rates for persistence diagram estimation in topological data analysis. Journal of Machine Learning Research, 16(1), 3603-3635.
  • Bubenik, P. (2015). Statistical topological data analysis using persistence landscapes. Journal of Machine Learning Research, 16(1), 77-102.
  • Reininghaus, J., Huber, S., Bauer, U., & Kwitt, R. (2015). A stable multi-scale kernel for topological machine learning. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (pp. 4741-4748).
  • Kwitt, R., Huber, S., Niethammer, M., Lin, W., & Bauer, U. (2015). Statistical topological data analysis-a kernel perspective. In Advances in Neural Information Processing Systems (pp. 3070-3078).

Software

See also

Other Resources