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We develop a framework for comparing data manifolds, aimed, in particular, towards the evaluation of deep generative models.
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Serguei Barannikov · 1994
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Laplacian eigenmaps and spectral techniques for embedding and clustering
Mikhail Belkin and Partha Niyogi · 2001
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Geometry helps in bottleneck matching and related problems
Alon Efrat, Alon Itai, and Matthew J Katz · 2001
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Computing and comprehending topology: Persistence and hierarchical Morse complexes (Ph.D.Thesis)
Afra J Zomorodian · 2001
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Algebraic topology
Allen Hatcher · 2005
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Computing persistent homology
Afra Zomorodian and Gunnar Carlsson · 2005
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Finding the homology of submanifolds with high confidence from random samples
Partha Niyogi, Stephen Smale, and Shmuel Weinberger · 2008
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Generative adversarial networks, 2014
Ian J. Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio · 2014
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Shapenet: An information-rich 3d model repository
Angel X Chang, Thomas Funkhouser, Leonidas Guibas, Pat Hanrahan, Qixing Huang, Zimo Li, Silvio Savarese, Manolis Savva, Shuran Song, Hao Su, et al · 2015
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A note on the evaluation of generative models
Lucas Theis, Aäron van den Oord, and Matthias Bethge · 2015
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Deep learning
Ian Goodfellow, Yoshua Bengio, Aaron Courville, and Yoshua Bengio · 2016
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Improved techniques for training gans
Tim Salimans, Ian Goodfellow, Wojciech Zaremba, Vicki Cheung, Alec Radford, and Xi Chen · 2016
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Geometric deep learning: Going beyond euclidean data
Michael M. Bronstein, Joan Bruna, Yann LeCun, Arthur Szlam, and Pierre Vandergheynst · 2017
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An introduction to topological data analysis: fundamental and practical aspects for data scientists
Frédéric Chazal and Bertrand Michel · 2017
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Gans trained by a two time-scale update rule converge to a local nash equilibrium
Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter · 2017
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Conditional image synthesis with auxiliary classifier gans
Augustus Odena, Christopher Olah, and Jonathon Shlens · 2017
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Learning representations and generative models for 3d point clouds
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Improved precision and recall metric for assessing generative models
Tuomas Kynkäänniemi, Tero Karras, Samuli Laine, Jaakko Lehtinen, and Timo Aila · 2019
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Computational Topology for Biomedical Image and Data Analysis: Theory and Applications
Rodrigo Rojas Moraleda, Nektarios A Valous, Wei Xiong, and Niels Halama · 2019
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Classification accuracy score for conditional generative models
Suman Ravuri and Oriol Vinyals · 2019
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The shape of data: Intrinsic distance for data distributions
Anton Tsitsulin, Marina Munkhoeva, Davide Mottin, Panagiotis Karras, Alex Bronstein, Ivan Oseledets, and Emmanuel Mueller · 2019
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Time-series generative adversarial networks
Jinsung Yoon, Daniel Jarrett, and Mihaela van der Schaar · 2019
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Mikołaj Bińkowski, Dougal J Sutherland, Michael Arbel, and Arthur Gretton · 2018
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Geometry score: A method for comparing generative adversarial networks
Valentin Khrulkov and Ivan Oseledets · 2018
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Are gans created equal? A large-scale study
Mario Lucic, Karol Kurach, Marcin Michalski, Sylvain Gelly, and Olivier Bousquet · 2018
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Skill rating for generative models
Catherine Olsson, Surya Bhupatiraju, Tom Brown, Augustus Odena, and Ian Goodfellow · 2018
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Pros and cons of gan evaluation measures
Ali Borji · 2019
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A domain agnostic measure for monitoring and evaluating gans
Paulina Grnarova, Kfir Y Levy, Aurelien Lucchi, Nathanael Perraudin, Ian Goodfellow, Thomas Hofmann, and Andreas Krause · 2019
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A style-based generator architecture for generative adversarial networks
Tero Karras, Samuli Laine, and Timo Aila · 2019
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Analyzing and improving the image quality of StyleGAN
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PLLay: Efficient topological layer based on persistence landscapes
Kwangho Kim, Jisu Kim, Manzil Zaheer, Joon Kim, Frédéric Chazal, and Larry Wasserman · 2020
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Topological autoencoders
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Covidgan: data augmentation using auxiliary classifier gan for improved covid-19 detection
Abdul Waheed, Muskan Goyal, Deepak Gupta, Ashish Khanna, Fadi Al-Turjman, and Plácido Rogerio Pinheiro · 2020
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Gpu-accelerated computation of Vietoris-Rips persistence barcodes
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Canonical Forms = Persistence Diagrams. Tutorial
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