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It is widely believed that natural image data exhibits low-dimensional structure despite the high dimensionality of conventional pixel representations.
The measure of the critical values of differentiable maps
Arthur Sard · 1942
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The statistics of natural images
Daniel L Ruderman · 1994
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Bruno A Olshausen and David J Field · 1996
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Nonlinear component analysis as a kernel eigenvalue problem
Bernhard Schölkopf, Alexander Smola, and Klaus-Robert Müller · 1998
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Sam T Roweis and Lawrence K Saul · 2000
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A global geometric framework for nonlinear dimensionality reduction
Joshua B Tenenbaum, Vin De Silva, and John C Langford · 2000
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Intrinsic Parameterizations of Surface Meshes
Mathieu Desbrun, Mark Meyer, and Pierre Alliez · 2002
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A survey of dimension reduction techniques
Imola K Fodor · 2002
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Charting a manifold
Matthew Brand · 2003
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The nonlinear statistics of high-contrast patches in natural images
Ann B. Lee, Kim S. Pedersen, and David Mumford · 2003
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Image manifolds which are isometric to Euclidean space
David L. Donoho and Carrie Grimes · 2005
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Maximum likelihood estimation of intrinsic dimension
Elizaveta Levina and Peter J Bickel · 2005
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Comments on ‘Maximum Likelihood Estimation of Intrinsic Dimension’ by E. Levina and P. Bickel (2004), 2005
David J.C. MacKay and Zoubin Ghahramani · 2005
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Reducing the dimensionality of data with neural networks
Geoffrey E Hinton and Ruslan R Salakhutdinov · 2006
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On the local behavior of spaces of natural images
Gunnar Carlsson, Tigran Ishkhanov, Vin de Silva, and Afra Zomorodian · 2008
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ImageNet: A large-scale hierarchical image database
Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei · 2009
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Learning multiple layers of features from tiny images
Alex Krizhevsky, Geoffrey Hinton, et al · 2009
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On the sample complexity of learning smooth cuts on a manifold
Hariharan Narayanan and Partha Niyogi · 2009
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Manifold models for signals and images
Gabriel Peyré · 2009
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Sample complexity of testing the manifold hypothesis
Hariharan Narayanan and Sanjoy Mitter · 2010
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Crystal fingerprint space – a novel paradigm for studying crystal-structure sets
Mario Valle and Artem R. Oganov · 2010
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Estimating the intrinsic dimension of datasets by a minimal neighborhood information
Elena Facco, Maria d’Errico, Alex Rodriguez, and Alessandro Laio · 2017
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Large scale GAN training for high fidelity natural image synthesis
Andrew Brock, Jeff Donahue, and Karen Simonyan · 2018
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Robert Geirhos, Patricia Rubisch, Claudio Michaelis, Matthias Bethge, Felix A Wichmann, and Wieland Brendel · 2018
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Francisco J Gonzalez and Maciej Balajewicz · 2018
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LDMNet: Low dimensional manifold regularized neural networks
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Reading digits in natural images with unsupervised feature learning
Yuval Netzer, Tao Wang, Adam Coates, Alessandro Bissacco, Bo Wu, and Andrew Y. Ng · 2011
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The MNIST database of handwritten digit images for machine learning research [best of the web]
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The intrinsic dimensionality of plant traits and its relevance to community assembly
Daniel C. Laughlin · 2014
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Microsoft COCO: Common objects in context
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Deep learning face attributes in the wild
Ziwei Liu, Ping Luo, Xiaogang Wang, and Xiaoou Tang · 2015
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Testing the manifold hypothesis
Charles Fefferman, Sanjoy Mitter, and Hariharan Narayanan · 2016
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Wei Zhu, Qiang Qiu, Jiaji Huang, Robert Calderbank, Guillermo Sapiro, and Ingrid Daubechies · 2018
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Intrinsic dimension of data representations in deep neural networks
Alessio Ansuini, Alessandro Laio, Jakob H Macke, and Davide Zoccolan · 2019
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Franz Besold and Vladimir Spokoiny · 2019
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Approximating cnns with bag-of-local-features models works surprisingly well on imagenet
Wieland Brendel and Matthias Bethge · 2019
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Geometry-aware maximum likelihood estimation of intrinsic dimension
Marina Gomtsyan, Nikita Mokrov, Maxim Panov, and Yury Yanovich · 2019
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On the intrinsic dimensionality of image representations
Sixue Gong, Vishnu Naresh Boddeti, and Anil K Jain · 2019
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Understanding generalization through visualizations, 2019
W. Ronny Huang, Zeyad Emam, Micah Goldblum, Liam Fowl, Justin K. Terry, Furong Huang, and Tom Goldstein · 2019
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Minimax Rates for Estimating the Dimension of a Manifold
Jisu Kim, Alessandro Rinaldo, and Larry Wasserman · 2019
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Disentangling adversarial robustness and generalization
David Stutz, Matthias Hein, and Bernt Schiele · 2019
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Combining mixture models with linear mixing updates: multilayer image segmentation and synthesis
Jonathan Vacher and Ruben Coen-Cagli · 2019
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Texture interpolation for probing visual perception
Jonathan Vacher, Aida Davila, Adam Kohn, and Ruben Coen-Cagli · 2020
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