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One of the main challenges of Topological Data Analysis (TDA) is to extract features from persistent diagrams directly usable by machine learning algorithms.
Extending Persistence Using Poincaré and Lefschetz Duality
David Cohen-Steiner, Herbert Edelsbrunner, and John Harer · 2009
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Simon Haykin · 2010
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Elementary Applied Topology
Robert Ghrist · 2014
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The gudhi library: Simplicial complexes and persistent homology
Clément Maria, Jean-Daniel Boissonnat, Marc Glisse, and Mariette Yvinec · 2014
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Statistical topological data analysis using persistence landscapes
Peter Bubenik · 2015
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Persistent homology and many-body atomic structure for medium-range order in the glass
Takenobu Nakamura, Yasuaki Hiraoka, Akihiko Hirata, Emerson G. Escolar, and Yasumasa Nishiura · 2015
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Persistence Theory: From Quiver Representations to Data Analysis
Steve Y. Oudot · 2015
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A stable multi-scale kernel for topological machine learning
Jan Reininghaus, Stefan Huber, Ulrich Bauer, and Roland Kwitt · 2015
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Deep learning
Ian Goodfellow, Yoshua Bengio, and Aaron Courville · 2016
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Persistence weighted gaussian kernel for topological data analysis
Genki Kusano, Yasuaki Hiraoka, and Kenji Fukumizu · 2016
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Persistence images: A stable vector representation of persistent homology
Henry Adams, Tegan Emerson, Michael Kirby, Rachel Neville, Chris Peterson, Patrick Shipman, Sofya Chepushtanova, Eric Hanson, Francis Motta, and Lori Ziegelmeier · 2017
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Sliced Wasserstein kernel for persistence diagrams
Mathieu Carrière, Marco Cuturi, and Steve Oudot · 2017
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Sliced Wasserstein kernel for persistence diagrams
Mathieu Carrière, Marco Cuturi, and Steve Oudot · 2017
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Deep Learning with Topological Signatures
Christoph Hofer, Roland Kwitt, Marc Niethammer, and Andreas Uhl · 2017
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Quantifying similarity of pore-geometry in nanoporous materials
Yongjin Lee, Senja D. Barthel, Paweł Dłotko, S. Mohamad Moosavi, Kathryn Hess, and Berend Smit · 2017
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Pointnet: Deep learning on point sets for 3d classification and segmentation
Charles R Qi, Hao Su, Kaichun Mo, and Leonidas J Guibas · 2017
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Cliques of Neurons Bound into Cavities Provide a Missing Link between Structure and Function
Michael W. Reimann, Max Nolte, Martina Scolamiero, Katharine Turner, Rodrigo Perin, Giuseppe Chindemi, Paweł Dłotko, Ran Levi, Kathryn Hess, and Henry Markram · 2017
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Attention is All You Need
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Łukasz Kaiser, and Illia Polosukhin · 2017
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Deep sets
Persistent homology detects curvature
Peter Bubenik, Michael Hull, Dhruv Patel, and Benjamin Whittle · 2020
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Language Models are Few-Shot Learners
Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, Sandhini Agarwal, Ariel Herbert-Voss, Gretchen Krueger, Tom Henighan, Rewon Child, Aditya Ramesh, Daniel Ziegler, Jeffrey Wu, Clemens Winter, Chris Hesse, Mark Chen, Eric Sigler, Mateusz Litwin, Scott Gray, Benjamin Chess, Jack Clark, Christopher Berner, Sam McCandlish, Alec Radford, Ilya Sutskever, and Dario Amodei · 2020
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PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures
Mathieu Carrière, Frédéric Chazal, Yuichi Ike, Théo Lacombe, Martin Royer, and Yuhei Umeda · 2020
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Visualising the Evolution of English Covid-19 Cases with Topological Data Analysis Ball Mapper, 2020
Pawel Dlotko and Simon Rudkin · 2020
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PLLay: Efficient Topological Layer based on Persistent Landscapes
Kwangho Kim, Jisu Kim, Manzil Zaheer, Joon Kim, Frederic Chazal, and Larry Wasserman · 2020
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Manzil Zaheer, Satwik Kottur, Siamak Ravanbhakhsh, Barnabás Póczos, Ruslan Salakhutdinov, and Alexander J. Smola · 2017
Cited alongside, same era.
Kernel method for persistence diagrams via kernel embedding and weight factor
Genki Kusano, Kenji Fukumizu, and Yasuaki Hiraoka · 2018
Cited alongside, same era.
Persistence fisher kernel: A Riemannian manifold kernel for persistence diagrams
Tam Le and Makoto Yamada · 2018
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Training Tips for the Transformer Model
Martin Popel and Ondřej Bojar · 2018
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BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding
Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova · 2019
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Learning Representations of Persistence Barcodes
Christoph D. Hofer, Roland Kwitt, and Marc Niethammer · 2019
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Set transformer: A framework for attention-based permutation-invariant neural networks
Juho Lee, Yoonho Lee, Jungtaek Kim, Adam Kosiorek, Seungjin Choi, and Yee Whye Teh · 2019
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Topology of deep neural networks
Gregory Naitzat, Andrey Zhitnikov, and Lek-Heng Lim · 2020
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Universal Approximation Power of Deep Neural Networks via Nonlinear Control Theory
Paulo Tabuada and Bahman Gharesifard · 2020
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Computational Topology for Data Analysis
Tamal Krishna Dey and Yusu Wang · 2021
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Topological Uncertainty: Monitoring trained neural networks through persistence of activation graphs
Théo Lacombe, Yuichi Ike, and Yuhei Umeda · 2021
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The space of persistence diagrams on n n points coarsely embeds into Hilbert space
Atish Mitra and Žiga Virk · 2021
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giotto-tda: A topological data analysis toolkit for machine learning and data exploration, 2021
Guillaume Tauzin, Umberto Lupo, Lewis Tunstall, Julian Burella Pérez, Matteo Caorsi, Wojciech Reise, Anibal Medina-Mardones, Alberto Dassatti, and Kathryn Hess · 2021
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Xiaohua Zhai, Alexander Kolesnikov, Neil Houlsby, and Lucas Beyer · 2021
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Giotto-deep: Deep learning made topological
Raphael Reinauer, Matteo Caorsi, and Nicolas Berkouk · 2022
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