Stability Analysis of Denoising Autoencoders Based on Dynamical Projection System
In this study, we give a stability analysis of denoising autoencoder(DAE) from the novel perspective of dynamical systems when the input density is defined as a distribution on a manifold. We demonstrate the connection between the corrupted distribution and the learned reconstruction function of a n...
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| Vydáno v: | IEEE transactions on knowledge and data engineering Ročník 33; číslo 8; s. 3155 - 3159 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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New York
IEEE
01.08.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 1041-4347, 1558-2191 |
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| Abstract | In this study, we give a stability analysis of denoising autoencoder(DAE) from the novel perspective of dynamical systems when the input density is defined as a distribution on a manifold. We demonstrate the connection between the corrupted distribution and the learned reconstruction function of a nonlinear DAE, which motivates the use of a dynamic projection system (DPS) associated with the learned reconstruction function. Utilizing the constructed DPS, we prove that the high-density region of the corrupted data distribution asymptotically converges to the data manifold. Then, we show that the region is the attracting stable equilibrium manifold of the DPS which is completely stable. These results serve a theoretical basis of the DAE in recognizing the high-density region of the highly corrupted data with large deviations through the DPS. The effectiveness of this analysis is verified by conducting experiments on several toy examples and real image datasets with various types of noise. |
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| AbstractList | In this study, we give a stability analysis of denoising autoencoder(DAE) from the novel perspective of dynamical systems when the input density is defined as a distribution on a manifold. We demonstrate the connection between the corrupted distribution and the learned reconstruction function of a nonlinear DAE, which motivates the use of a dynamic projection system (DPS) associated with the learned reconstruction function. Utilizing the constructed DPS, we prove that the high-density region of the corrupted data distribution asymptotically converges to the data manifold. Then, we show that the region is the attracting stable equilibrium manifold of the DPS which is completely stable. These results serve a theoretical basis of the DAE in recognizing the high-density region of the highly corrupted data with large deviations through the DPS. The effectiveness of this analysis is verified by conducting experiments on several toy examples and real image datasets with various types of noise. |
| Author | Park, Saerom Lee, Jaewook |
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| References | bojchevski (ref13) 2017 kurakin (ref21) 2017 ref15 ref11 lecun (ref18) 2010; 2 ref10 xiao (ref19) 2017 ref2 madry (ref22) 2018 zhang (ref17) 2007 ref1 ref16 ref7 krizhevsky (ref20) 2009 bracewell (ref14) 1999 ref4 ref3 maaten (ref6) 2008; 9 goodfellow (ref8) 2016 alain (ref9) 2014; 15 kingma (ref12) 2010 roweis (ref5) 2000; 290 |
| References_xml | – year: 2018 ident: ref22 article-title: Towards deep learning models resistant to adversarial attacks publication-title: Proc Int Conf Learn Representations – ident: ref7 doi: 10.1162/089976603321780317 – year: 2017 ident: ref21 article-title: Adversarial machine learning at scale publication-title: Proc Int Conf Learn Representations – ident: ref3 doi: 10.1162/089976698300017467 – year: 2017 ident: ref13 article-title: Learning by denoising part 2. connection between data distribution and denoising function – year: 2017 ident: ref19 article-title: Fashion-MNIST: A novel image dataset for benchmarking machine learning algorithms – volume: 15 start-page: 3563 year: 2014 ident: ref9 article-title: What regularized auto-encoders learn from the data-generating distribution publication-title: J Mach Learn Res – ident: ref15 doi: 10.1109/TAC.2004.829603 – ident: ref10 doi: 10.1109/TPAMI.2014.2362140 – year: 2016 ident: ref8 publication-title: Deep Learning – start-page: 1126 year: 2010 ident: ref12 article-title: Regularized estimation of image statistics by score matching publication-title: Proc Advances Neural Inf Process Syst – ident: ref1 doi: 10.1080/14786440109462720 – ident: ref16 doi: 10.1109/81.983867 – start-page: 1593 year: 2007 ident: ref17 article-title: Mlle: Modified locally linear embedding using multiple weights publication-title: Proc Advances Neural Inf Process Syst – volume: 9 start-page: 2579 year: 2008 ident: ref6 article-title: Visualizing data using t-SNE publication-title: J Mach Learn Res – ident: ref11 doi: 10.1109/TPAMI.2014.2318727 – year: 2009 ident: ref20 article-title: Learning multiple layers of features from tiny images – start-page: 74 year: 1999 ident: ref14 article-title: The sifting property publication-title: The Fourier Transform and Its Applications – volume: 290 start-page: 2323 year: 2000 ident: ref5 article-title: Nonlinear dimensionality reduction by locally linear embedding publication-title: Science doi: 10.1126/science.290.5500.2323 – ident: ref4 doi: 10.1126/science.290.5500.2319 – volume: 2 year: 2010 ident: ref18 article-title: MNIST handwritten digit database publication-title: AT&T Labs – ident: ref2 doi: 10.1007/BF02288916 |
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| SubjectTerms | autoencoders data manifold Data models Density Dynamic stability dynamical systems Image reconstruction Manifolds Noise measurement Noise reduction Nonlinear projection Perturbation methods Reconstruction Stability analysis |
| Title | Stability Analysis of Denoising Autoencoders Based on Dynamical Projection System |
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