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Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning.
“Ridge Regression: Biased Estimation for Nonorthogonal Problems”
Arthur. Hoerl and Robert. Kennard · 1970
Earlier work this paper cites.
“Nonlinear total variation based noise removal algorithms”
Leonid. Rudin, Stanley Osher and Emad Fatemi · 1992
Earlier work this paper cites.
“Regression Shrinkage and Selection via the Lasso”
Robert Tibshirani · 1996
Earlier work this paper cites.
“Persistence barcodes for shapes”
Gunnar Carlsson, Afra Zomorodian, Anne Collins and Leonidas Guibas · 2005
Earlier work this paper cites.
“Computing Persistent Homology”
Afra Zomorodian and Gunnar Carlsson · 2005
Earlier work this paper cites.
“Introduction to Algorithms”
Thomas. Cormen, Charles. Leiserson, Ronald. Rivest and Clifford Stein · 2009
Earlier work this paper cites.
“Persistent heat signature for pose-oblivious matching of incomplete models”
Tamal Dey et al · 2010
Earlier work this paper cites.
“Alpha Shapes – a Survey”
Herbert Edelsbrunner · 2010
Earlier work this paper cites.
“Computational Topology - an Introduction.”
Herbert Edelsbrunner and John Harer · 2010
Earlier work this paper cites.
“Persistence-based segmentation of deformable shapes”
Primoz Skraba, Maks Ovsjanikov, Frederic Chazal and Leonidas Guibas · 2010
Earlier work this paper cites.
“Nearly-Isotonic Regression”
Ryan. Tibshirani, Holger Hoefling and Robert Tibshirani · 2010
Earlier work this paper cites.
“Dualities in persistent (co)homology”
Vin deSilva, Dimitriy Morozov and Mikael Vejdemo-Johansson · 2011
Earlier work this paper cites.
“Zigzag persistent homology in matrix multiplication time”
Nikola Milosavljević, Dmitriy Morozov and Primoz Skraba · 2011
Earlier work this paper cites.
“Generative adversarial nets”
Ian. Goodfellow et al · 2014
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“Explaining and Harnessing Adversarial Examples”
Ian Goodfellow, Jonathon Shlens and Christian Szegedy · 2015
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“The ring of algebraic functions on persistence bar codes”
Aaron Adcock, Erik Carlsson and Gunnar Carlsson · 2016
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“Infogan: Interpretable representation learning by information maximizing generative adversarial nets”
Xi Chen et al · 2016
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“Applying Topological Persistence in Convolutional Neural Network for Music Audio Signals”
Jen-Yu Liu, Shyh-Kang Jeng and Yi-Hsuan Yang · 2016
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“Learning Representations and Generative Models for 3D Point Clouds”
Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas and Leonidas Guibas · 2018
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“Exposition and Interpretation of the Topology of Neural Networks”
Rickard Brüel-Gabrielsson and Gunnar Carlsson · 2018
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“Topological Approaches to Deep Learning”
Gunnar Carlsson and Rickard Brüel-Gabrielsson · 2018
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“Adversarial Attacks and Defences: A Survey”
Anirban Chakraborty et al · 2018
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“On Characterizing the Capacity of Neural Networks using Algebraic Topology”
William. Guss and Ruslan Salakhutdinov · 2018
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Tim Salimans et al · 2016
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“Learning a probabilistic latent space of object shapes via 3d generative-adversarial modeling”
Jiajun Wu et al · 2016
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“Adversary Detection in Neural Networks via Persistent Homology”
Thomas Gebhart and Paul Schrater · 2017
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“Persistent homology machine learning for fingerprint classification”
Noah Giansiracusa, Robert Giansiracusa and Chul Moon · 2017
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“Deep Learning with Topological Signatures”
Christoph Hofer and et al · 2017
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“A roadmap for the computation of persistent homology”
Nina Otter et al · 2017
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“Automatic Differentiation in PyTorch”
Adam Paszke et al · 2017
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“Topological Function Optimization for Continuous Shape Matching”
Adrien Poulenard, Primoz Skraba and Maks Ovsjanikov · 2018
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“Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology”
Bastian Rieck et al · 2018
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“Persistent-Homology-based Machine Learning and its Applications – A Survey”
Chi Seng, Kelin Xia and Si Xian · 2018
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“Topology-Aware Surface Reconstruction for Point Clouds”
Rickard Brüel-Gabrielsson, Vignesh Ganapathi-Subramanian, Primoz Skraba and Lenoidas Guibas · 2019
Closest in time.
“A Topological Regularizer for Classifiers via Persistent Homology”
Chao Chen, Xiuyan Ni, Qinxun Bai and Yusu Wang · 2019
Closest in time.
“Explicit topological priors for deep-learning based image segmentation using persistent homology”
James. Clough et al · 2019
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“Topology of Learning in Artificial Neural Networks”
Maxime Gabella, Nitya Afambo, Stefania Ebli and Gard Spreemann · 2019
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“Adversarial Examples Target Topological Holes in Deep Networks”
Thomas Gebhart and Paul Schrater · 2019
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