Topological Data Analysis

For students interested in working with me on TDA projects, here are some suggested resources to learn about the field.

Videos

• Applied Algebraic Topology Research Network YouTube Channel:  https://www.youtube.com/@aatrn1

• Socratica Course on Group Theory:  https://www.socratica.com/courses/group-theory

Papers - Overview

• Wasserman, L., 2018. Topological data analysis. Annual Review of Statistics and Its Application, 5(1), pp.501-532.

  • Also, see Larry's blog post on the topic:  https://normaldeviate.wordpress.com/2012/07/01/topological-data-analysis/

• Otter, N., Porter, M.A., Tillmann, U., Grindrod, P. and Harrington, H.A., 2017. A roadmap for the computation of persistent homology. EPJ Data Science, 6, pp.1-38.

  • Overview of persistent homology computations.

• Zhu, X., 2013, August. Persistent homology: An introduction and a new text representation for natural language processing. In IJCAI (No. 2013, pp. 1953-1959).

  • Great introduction to persistent homology.

• Fasy, B.T., Lecci, F., Rinaldo, A., Wasserman, L., Balakrishnan, S. and Singh, A., 2014. CONFIDENCE SETS FOR PERSISTENCE DIAGRAMS. The Annals of Statistics, pp.2301-2339.

  • An inference method on the space of persistence diagrams.

• Mileyko, Y., Mukherjee, S. and Harer, J., 2011. Probability measures on the space of persistence diagrams. Inverse Problems, 27(12), p.124007.

Papers - Functional Summaries

• Berry, E., Chen, Y.C., Cisewski-Kehe, J. and Fasy, B.T., 2020. Functional summaries of persistence diagrams. Journal of Applied and Computational Topology, 4(2), pp.211-262.

  • Code:  https://github.com/JessiCisewskiKehe/generalized_landscapes

• Bubenik, P., 2015. Statistical topological data analysis using persistence landscapes. J. Mach. Learn. Res., 16(1), pp.77-102.

Papers - Astronomy

• Green, S.B., Mintz, A., Xu, X. and Cisewski-Kehe, J., 2019. Topology of our cosmology with persistent homology. Chance, 32(3), pp.6-13.

  • This article is intended to be a relatively non-technical introduction to a general statistics audience.

• Xu, X., Cisewski-Kehe, J., Green, S.B. and Nagai, D., 2019. Finding cosmic voids and filament loops using topological data analysis. Astronomy and Computing, 27, pp.34-52.

  • Code:  https://github.com/xinxuyale/SCHU

• Cisewski-Kehe, J., Fasy, B.T., Hellwing, W., Lovell, M.R., Drozda, P. and Wu, M., 2022. Differentiating small-scale subhalo distributions in CDM and WDM models using persistent homology. Physical Review D, 106(2), p.023521.

  • Code:  https://github.com/JessiCisewskiKehe/DarkMatterTDA

• Van De Weygaert, R., Vegter, G., Edelsbrunner, H., Jones, B.J., Pranav, P., Park, C., Hellwing, W.A., Eldering, B., Kruithof, N., Bos, E.G.P. and Hidding, J., 2011. Alpha, betti and the megaparsec universe: on the topology of the cosmic web. Transactions on Computational Science XIV: Special Issue on Voronoi Diagrams and Delaunay Triangulation, pp.60-101.

Papers - topological shape analysis

• Turner, K., Mukherjee, S. and Boyer, D.M., 2014. Persistent homology transform for modeling shapes and surfaces. Information and Inference: A Journal of the IMA, 3(4), pp.310-344.

• Jiang, Q., Kurtek, S. and Needham, T., 2020. The weighted Euler curve transform for shape and image analysis. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (pp. 844-845).