References
Adams, Henry, Tegan Emerson, Michael Kirby, et al. 2017.
“Persistence Images: A Stable Vector Representation of Persistent
Homology.” Journal of Machine Learning Research 18 (8):
1–35. https://www.jmlr.org/papers/v18/16-337.html.
Andrews, David F., and Agnes M. Herzberg. 1985. Data: A Collection
of Problems from Many Fields for the Student and Research Worker.
Springer. https://doi.org/10.1007/978-1-4612-5098-2.
Bubenik, Peter. 2015. “Statistical Topological Data Analysis Using
Persistence Landscapes.” Journal of Machine Learning
Research 16 (3): 77–102. https://www.jmlr.org/papers/v16/bubenik15a.html.
Carlsson, Gunnar. 2009. “Topology and Data.” Bulletin
of the American Mathematical Society 46 (2): 255–308. https://doi.org/10.1090/S0273-0979-09-01249-X.
Carlsson, Gunnar, and Mikael Vejdemo-Johansson. 2021. Topological
Data Analysis with Applications. Cambridge University Press. https://doi.org/10.1017/9781108975704.
Chazal, Frédéric, Leonidas J. Guibas, Steve Y. Oudot, and Primož Škraba.
2013. “Persistence-Based Clustering in Riemannian
Manifolds.” Journal of the ACM 60 (6): 1–38. https://doi.org/10.1145/2535927.
Chazal, Frédéric, Vin de Silva, and Steve Oudot. 2014.
“Persistence Stability for Geometric Complexes.”
Geometriae Dedicata 173: 193–214. https://doi.org/10.1007/s10711-013-9937-z.
Cohen-Steiner, David, Herbert Edelsbrunner, and John Harer. 2007.
“Stability of Persistence Diagrams.” Discrete &
Computational Geometry 37 (1): 103–20. https://doi.org/10.1007/s00454-006-1276-5.
Crawley-Boevey, William. 2015. “Decomposition of Pointwise
Finite-Dimensional Persistence Modules.” Proceedings of the
American Mathematical Society 143: 555–65. https://arxiv.org/abs/1210.0819.
Dłotko, Paweł. 2019. Ball Mapper: A Shape Summary for Topological
Data Analysis. https://doi.org/10.48550/arXiv.1901.07410.
Edelsbrunner, Herbert, and John Harer. 2010. Computational Topology:
An Introduction. American Mathematical Society.
Ester, Martin, Hans-Peter Kriegel, Jörg Sander, and Xiaowei Xu. 1996.
“A Density-Based Algorithm for Discovering Clusters in Large
Spatial Databases with Noise.” Proceedings of the Second
International Conference on Knowledge Discovery and Data Mining,
226–31. https://cdn.aaai.org/KDD/1996/KDD96-037.pdf.
Fasy, Brittany Terese, Fabrizio Lecci, Alessandro Rinaldo, Larry
Wasserman, Sivaraman Balakrishnan, and Aarti Singh. 2014.
“Confidence Sets for Persistence Diagrams.” The Annals
of Statistics 42 (6): 2301–39. https://doi.org/10.1214/14-AOS1252.
Fisher, Ronald A. 1936a. Iris. UCI Machine Learning Repository.
https://doi.org/10.24432/C56C76.
Fisher, Ronald A. 1936b. “The Use of Multiple Measurements in
Taxonomic Problems.” Annals of Eugenics 7 (2): 179–88.
https://doi.org/10.1111/j.1469-1809.1936.tb02137.x.
Gakhar, Hitesh, and Jose A. Perea. 2024. “Sliding Window
Persistence of Quasiperiodic Functions.” Journal of Applied
and Computational Topology 8 (1): 55–92. https://doi.org/10.1007/s41468-023-00136-7.
Ghrist, Robert. 2008. “Barcodes: The Persistent Topology of
Data.” Bulletin of the American Mathematical Society 45
(1): 61–75. https://doi.org/10.1090/S0273-0979-07-01191-3.
Ghrist, Robert. 2014. Elementary Applied Topology. https://www2.math.upenn.edu/~ghrist/notes.html.
Hatcher, Allen. 2002. Algebraic Topology. Cambridge University
Press. https://pi.math.cornell.edu/~hatcher/AT/ATpage.html.
Nicolau, Monica, Arnold J. Levine, and Gunnar Carlsson. 2011.
“Topology Based Data Analysis Identifies a Subgroup of Breast
Cancers with a Unique Mutational Profile and Excellent Survival.”
Proceedings of the National Academy of Sciences 108 (17):
7265–70. https://doi.org/10.1073/pnas.1102826108.
Perea, Jose A., and John Harer. 2015. “Sliding Windows and
Persistence: An Application of Topological Methods to Signal
Analysis.” Foundations of Computational Mathematics 15
(3): 799–838. https://doi.org/10.1007/s10208-014-9206-z.
Reaven, G. M., and R. G. Miller. 1979. “An Attempt to Define the
Nature of Chemical Diabetes Using a Multidimensional Analysis.”
Diabetologia 16: 17–24.
Singh, Gurjeet, Facundo Mémoli, and Gunnar Carlsson. 2007.
“Topological Methods for the Analysis of High Dimensional Data
Sets and 3D Object Recognition.” Eurographics Symposium on
Point-Based Graphics, 91–100. https://doi.org/10.2312/SPBG/SPBG07/091-100.
Takens, Floris. 1981. “Detecting Strange Attractors in
Turbulence.” In Dynamical Systems and Turbulence, Warwick
1980, vol. 898. Lecture Notes in Mathematics. Springer. https://doi.org/10.1007/BFb0091924.
Ultsch, Alfred, and Jörn Lötsch. 2020. “The Fundamental Clustering
and Projection Suite (FCPS): A Dataset Collection to Test the
Performance of Clustering and Data Projection Algorithms.”
Data 5 (1): 13. https://doi.org/10.3390/data5010013.
Zomorodian, Afra J. 2005. Topology for Computing. Cambridge
University Press. https://www.cambridge.org/core/books/topology-for-computing/1171035B570105A57865CEA390BA5E74.