Geodesic Learning With Uniform Interpolation on Data Manifold
Recently with the development of deep learning on data representation and generation, how to sampling on a data manifold becomes a crucial problem for research. In this paper, we propose a method to learn a minimizing geodesic within a data manifold. Along the learned geodesic, our method is able to...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
IEEE
2022-01-01
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| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/9893107/ |
| _version_ | 1811258528835305472 |
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| author | Cong Geng Jia Wang Li Chen Zhiyong Gao |
| author_facet | Cong Geng Jia Wang Li Chen Zhiyong Gao |
| author_sort | Cong Geng |
| collection | DOAJ |
| description | Recently with the development of deep learning on data representation and generation, how to sampling on a data manifold becomes a crucial problem for research. In this paper, we propose a method to learn a minimizing geodesic within a data manifold. Along the learned geodesic, our method is able to generate high-quality uniform interpolations with the shortest path between two given data samples. Specifically, we use an autoencoder network to map data samples into the latent space and perform interpolation in the latent space via an interpolation network. We add prior geometric information to regularize our autoencoder for a flat latent embedding. The Riemannian metric on the data manifold is induced by the canonical metric in the Euclidean space in which the data manifold is isometrically immersed. Based on this defined Riemannian metric, we introduce a constant-speed loss and a minimizing geodesic loss to regularize the interpolation network to generate uniform interpolations along the learned geodesic on the manifold. We provide a theoretical analysis of our model and use image interpolation as an example to demonstrate the effectiveness of our method. |
| first_indexed | 2024-04-12T18:15:40Z |
| format | Article |
| id | doaj.art-29a0bc23e8dd49e8869b1ff38e0ebb6c |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-04-12T18:15:40Z |
| publishDate | 2022-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-29a0bc23e8dd49e8869b1ff38e0ebb6c2022-12-22T03:21:37ZengIEEEIEEE Access2169-35362022-01-0110986629866910.1109/ACCESS.2022.32067759893107Geodesic Learning With Uniform Interpolation on Data ManifoldCong Geng0Jia Wang1Li Chen2https://orcid.org/0000-0001-9899-2535Zhiyong Gao3Institute of Image Communication and Network Engineering, Shanghai Jiao Tong University, Shanghai, ChinaInstitute of Image Communication and Network Engineering, Shanghai Jiao Tong University, Shanghai, ChinaInstitute of Image Communication and Network Engineering, Shanghai Jiao Tong University, Shanghai, ChinaInstitute of Image Communication and Network Engineering, Shanghai Jiao Tong University, Shanghai, ChinaRecently with the development of deep learning on data representation and generation, how to sampling on a data manifold becomes a crucial problem for research. In this paper, we propose a method to learn a minimizing geodesic within a data manifold. Along the learned geodesic, our method is able to generate high-quality uniform interpolations with the shortest path between two given data samples. Specifically, we use an autoencoder network to map data samples into the latent space and perform interpolation in the latent space via an interpolation network. We add prior geometric information to regularize our autoencoder for a flat latent embedding. The Riemannian metric on the data manifold is induced by the canonical metric in the Euclidean space in which the data manifold is isometrically immersed. Based on this defined Riemannian metric, we introduce a constant-speed loss and a minimizing geodesic loss to regularize the interpolation network to generate uniform interpolations along the learned geodesic on the manifold. We provide a theoretical analysis of our model and use image interpolation as an example to demonstrate the effectiveness of our method.https://ieeexplore.ieee.org/document/9893107/Geodesic learninguniform interpolationflat embeddingautoencoderconstant-speed |
| spellingShingle | Cong Geng Jia Wang Li Chen Zhiyong Gao Geodesic Learning With Uniform Interpolation on Data Manifold IEEE Access Geodesic learning uniform interpolation flat embedding autoencoder constant-speed |
| title | Geodesic Learning With Uniform Interpolation on Data Manifold |
| title_full | Geodesic Learning With Uniform Interpolation on Data Manifold |
| title_fullStr | Geodesic Learning With Uniform Interpolation on Data Manifold |
| title_full_unstemmed | Geodesic Learning With Uniform Interpolation on Data Manifold |
| title_short | Geodesic Learning With Uniform Interpolation on Data Manifold |
| title_sort | geodesic learning with uniform interpolation on data manifold |
| topic | Geodesic learning uniform interpolation flat embedding autoencoder constant-speed |
| url | https://ieeexplore.ieee.org/document/9893107/ |
| work_keys_str_mv | AT conggeng geodesiclearningwithuniforminterpolationondatamanifold AT jiawang geodesiclearningwithuniforminterpolationondatamanifold AT lichen geodesiclearningwithuniforminterpolationondatamanifold AT zhiyonggao geodesiclearningwithuniforminterpolationondatamanifold |