Topological Data Analysis

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

Videos

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).