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Persistence diagrams, the most common descriptors of Topological Data Analysis, encode topological properties of data and have already proved pivotal in many different applications of data science.
Topolayout: Multilevel graph layout by topological features
Daniel Archambault, Tamara Munzner, and David Auber · 2007
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Dna microarrays: design principles for maximizing ergodic, chaotic mixing
Jan-Martin Hertzsch, Rob Sturman, and Stephen Wiggins · 2007
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Extending persistence using Poincaré and Lefschetz duality
David Cohen-Steiner, Herbert Edelsbrunner, and John Harer · 2009
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A concise and provably informative multi-scale signature based on heat diffusion
Jian Sun, Maks Ovsjanikov, and Leonidas Guibas · 2009
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Computational topology: an introduction
Herbert Edelsbrunner and John Harer · 2010
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Topological features of online social networks
Emilio Ferrara and Giacomo Fiumara · 2012
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Effective graph classification based on topological and label attributes
Geng Li, Murat Semerci, Bülent Yener, and Mohammed J Zaki · 2012
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Persistence stability for geometric complexes
Frédéric Chazal, Vin de Silva, and Steve Oudot · 2014
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Stable and informative spectral signatures for graph matching
Nan Hu, Raif Rustamov, and Leonidas Guibas · 2014
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Adam: a method for stochastic optimization
Diederik Kingma and Jimmy Ba · 2014
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Persistence-based structural recognition
Chunyuan Li, Maks Ovsjanikov, and Frédéric Chazal · 2014
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Statistical topological data analysis using persistence landscapes
Peter Bubenik · 2015
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Stochastic convergence of persistence landscapes and silhouettes
Frédéric Chazal, Brittany Terese Fasy, Fabrizio Lecci, Alessandro Rinaldo, and Larry Wasserman · 2015
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Stable topological signatures for points on 3d shapes
Mathieu Carrière, Steve Oudot, and Maks Ovsjanikov · 2015
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Persistence theory: from quiver representations to data analysis
Steve Oudot · 2015
Cited alongside, same era.
Sliding windows and persistence: an application of topological methods to signal analysis
Jose Perea and John Harer · 2015
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A stable multi-scale kernel for topological machine learning
Jan Reininghaus, Stefan Huber, Ulrich Bauer, and Roland Kwitt · 2015
Cited alongside, same era.
GUDHI User and Reference Manual
The GUDHI Project · 2015
Cited alongside, same era.
Deep graph kernels
Pinar Yanardag and S.V.N. Vishwanathan · 2015
Cited alongside, same era.
The structure and stability of persistence modules
Frédéric Chazal, Vin de Silva, Marc Glisse, and Steve Oudot · 2016
Cited alongside, same era.
Persistent homology and materials informatics
Mickaël Buchet, Yasuaki Hiraoka, and Ippei Obayashi · 2018
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Tropical coordinates on the space of persistence barcodes
Sara Kališnik · 2018
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Persistence Fisher kernel: a Riemannian manifold kernel for persistence diagrams
Tam Le and Makoto Yamada · 2018
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Netlsd: hearing the shape of a graph
Anton Tsitsulin, Davide Mottin, Panagiotis Karras, Alexander Bronstein, and Emmanuel Müller · 2018
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Scale-variant topological information for characterizing complex networks
Quoc Hoan Tran, Van Tuan Vo, and Yoshihiko Hasegawa · 2018
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RetGK: Graph Kernels based on Return Probabilities of Random Walks
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Persistence weighted Gaussian kernel for topological data analysis
Genki Kusano, Yasuaki Hiraoka, and Kenji Fukumizu · 2016
Cited alongside, same era.
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
Cited alongside, same era.
Topological methods for genomics: present and future directions
Pablo Cámara · 2017
Cited alongside, same era.
Sliced Wasserstein kernel for persistence diagrams
Mathieu Carrière, Marco Cuturi, and Steve Oudot · 2017
Cited alongside, same era.
Deep learning with topological signatures
Christoph Hofer, Roland Kwitt, Marc Niethammer, and Andreas Uhl · 2017
Cited alongside, same era.
Hunt for the unique, stable, sparse and fast feature learning on graphs
Saurabh Verma and Zhi-Li Zhang · 2017
Cited alongside, same era.
Zhen Zhang, Mianzhi Wang, Yijian Xiang, Yan Huang, and Arye Nehorai · 2018
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A topology layer for machine learning
Rickard Brüel-Gabrielsson, Bradley J Nelson, Anjan Dwaraknath, Primoz Skraba, Leonidas J Guibas, and Gunnar Carlsson · 2019
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Vincent Divol and Théo Lacombe · 2019
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Learning representations of persistence barcodes
Christoph D. Hofer, Roland Kwitt, and Marc Niethammer · 2019
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A framework for differential calculus on persistence barcodes, 2019
Jacob Leygonie, Steve Oudot, and Ulrike Tillmann · 2019
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Capsule graph neural network
Zhang Xinyi and Lihui Chen · 2019
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How powerful are graph neural networks?
Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka · 2019
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Learning metrics for persistence-based summaries and applications for graph classification
Qi Zhao and Yusu Wang · 2019
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