Building deep networks on grassmann manifolds
Learning representations on Grassmann manifolds is popular in quite a few visual recognition tasks. In order to enable deep learning on Grassmann manifolds, this paper proposes a deep network architecture by generalizing the Euclidean network paradigm to Grassmann manifolds. In particular, we design...
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sg-smu-ink.sis_research-75472022-01-10T03:43:12Z Building deep networks on grassmann manifolds HUANG, Zhiwu WU, J. VAN, Gool L. Learning representations on Grassmann manifolds is popular in quite a few visual recognition tasks. In order to enable deep learning on Grassmann manifolds, this paper proposes a deep network architecture by generalizing the Euclidean network paradigm to Grassmann manifolds. In particular, we design full rank mapping layers to transform input Grassmannian data to more desirable ones, exploit re-orthonormalization layers to normalize the resulting matrices, study projection pooling layers to reduce the model complexity in the Grassmannian context, and devise projection mapping layers to respect Grassmannian geometry and meanwhile achieve Euclidean forms for regular output layers. To train the Grassmann networks, we exploit a stochastic gradient descent setting on manifolds of the connection weights, and study a matrix generalization of backpropagation to update the structured data. The evaluations on three visual recognition tasks show that our Grassmann networks have clear advantages over existing Grassmann learning methods, and achieve results comparable with state-of-the-art approaches. 2018-02-01T08:00:00Z text application/pdf https://ink.library.smu.edu.sg/sis_research/6544 https://ink.library.smu.edu.sg/context/sis_research/article/7547/viewcontent/Building_Deep_Networks.pdf http://creativecommons.org/licenses/by-nc-nd/4.0/ Research Collection School Of Computing and Information Systems eng Institutional Knowledge at Singapore Management University Artificial intelligence; Mapping; Matrix algebra; Network architecture; Stochastic systems Artificial Intelligence and Robotics OS and Networks |
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Artificial intelligence; Mapping; Matrix algebra; Network architecture; Stochastic systems Artificial Intelligence and Robotics OS and Networks HUANG, Zhiwu WU, J. VAN, Gool L. Building deep networks on grassmann manifolds |
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Learning representations on Grassmann manifolds is popular in quite a few visual recognition tasks. In order to enable deep learning on Grassmann manifolds, this paper proposes a deep network architecture by generalizing the Euclidean network paradigm to Grassmann manifolds. In particular, we design full rank mapping layers to transform input Grassmannian data to more desirable ones, exploit re-orthonormalization layers to normalize the resulting matrices, study projection pooling layers to reduce the model complexity in the Grassmannian context, and devise projection mapping layers to respect Grassmannian geometry and meanwhile achieve Euclidean forms for regular output layers. To train the Grassmann networks, we exploit a stochastic gradient descent setting on manifolds of the connection weights, and study a matrix generalization of backpropagation to update the structured data. The evaluations on three visual recognition tasks show that our Grassmann networks have clear advantages over existing Grassmann learning methods, and achieve results comparable with state-of-the-art approaches. |
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text |
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HUANG, Zhiwu WU, J. VAN, Gool L. |
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HUANG, Zhiwu WU, J. VAN, Gool L. |
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HUANG, Zhiwu |
title |
Building deep networks on grassmann manifolds |
title_short |
Building deep networks on grassmann manifolds |
title_full |
Building deep networks on grassmann manifolds |
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Building deep networks on grassmann manifolds |
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Building deep networks on grassmann manifolds |
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building deep networks on grassmann manifolds |
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Institutional Knowledge at Singapore Management University |
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2018 |
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https://ink.library.smu.edu.sg/sis_research/6544 https://ink.library.smu.edu.sg/context/sis_research/article/7547/viewcontent/Building_Deep_Networks.pdf |
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