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ETEX01 Literature

Basic Literature

• R.Ghrist, Elementary Applied Topology, Createspace, 2014. Link
• A. Zomorodian and G. Carlsson, Computing Persistent Homology>, Discrete and Computational Geometry 33 (2005) 249-274. Link
• G. Carlsson, Persistent Homology and Applied Homotopy Theory, ArXiv 2020
• W. Byttner, Classifying RGB Images with multi-colour Persistent Homology LiTH-MAT-EX--2019/01--SE File
• H. Edelsbrunner, J. L. Harer, Computational Topology: An Introduction AMS, 2010. File
• Z. Virk, Introduction to Persistent Homology University of Ljubjana, 2022

Other References

• J. A. Perea, A Brief History of Persistent ArXiv:1809.03624v2 [math.AT]
• G. Carlsson Topology and Data, BULL. AMS,46,(2),2009,255–308
• G. Carlsson, V. de Silva, Zigzag Persistent , Found Comput Math, 10 (2010), 367–405 DOI: 10.1007/s10208-010-9066-0
• C.S. Pun, K. Xia, S. X. Lee Persistent Homology-based Machine Learning and its Applications - A Survey, DOI: 10.48550/arXiv.1811.00252
• H. Edelsbrunner, Alpha Shape, A Survey. File
• Otter et al. A roadmap for the computation of persistent homology EPJ Data Science (2017) 6:17 DOI 10.1140/epjds/s13688-017-0109-5
  
  This two books are classic in Algebraic Topology, both have very good collections of exercises.
  
• M. A. Armstrong, Basic Topology, Springer-Verlag, New Yok, 1983, Link to Internet Archive
• W. S. Massey A Basic Course in algebraic Topology. Springer-Verlag, New York 1991.

References for Examination Projects

• V. de Silva, R. Ghrist Coverage in sensor networks via persistent homology Algebr. Geom. Topol. 7(1), (2007), 339-358 DOI: 10.2140/agt.2007.7.339
• P. Niyogi, S. Smale, Shmuel Weinberger, Finding the Homology of Submanifolds with High Confidence from Random Samples Discrete Comput Geom (2008) 39: 419–441 DOI: 10.1007/s00454-008-9053-2
• T. K. Dey, T. Hou, Fast Computation of Zigzag Persistence DOI:10.48550/arXiv.2204.11080
• R. Antonova, A Varava, P. Shi, J. F. Carvalho, D. Kragic, Sequential Topological Representations for Predictive Models of Deformable Objects Proc. of Machine Learning Research vol 144:1–13, 2021
• N. Giansiracusa, R. Giansiracusa, C. Moon, Persistent homology machine learning for fingerprint classification. DOI: 10.48550/arXiv.1711.09158
• T. Qaiser, K. Sirinukunwattana, K. Nakane, Y-W. Tsang, D. Epstein, N. Rajpoo, Persistent Homology for Fast Tumor Segmentation in Whole Slide Histology Images Procedia Computer Science 90 (2016) 119 – 124

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Senast uppdaterad: 2024-10-02