Learning by Autonomous Manifold Deformation with an Intrinsic Deforming Field
A self-organized geometric model is proposed for data dimension reduction to improve the robustness of manifold learning. In the model, a novel mechanism for dimension reduction is presented by the autonomous deforming of data manifolds. The autonomous deforming vector field is proposed to guide the...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/11/1995 |
| _version_ | 1797457657072713728 |
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| author | Xiaodong Zhuang Nikos Mastorakis |
| author_facet | Xiaodong Zhuang Nikos Mastorakis |
| author_sort | Xiaodong Zhuang |
| collection | DOAJ |
| description | A self-organized geometric model is proposed for data dimension reduction to improve the robustness of manifold learning. In the model, a novel mechanism for dimension reduction is presented by the autonomous deforming of data manifolds. The autonomous deforming vector field is proposed to guide the deformation of the data manifold. The flattening of the data manifold is achieved as an emergent behavior under the virtual elastic and repulsive interaction between the data points. The manifold’s topological structure is preserved when it evolves to the shape of lower dimension. The soft neighborhood is proposed to overcome the uneven sampling and neighbor point misjudging problems. The simulation experiment results of data sets prove its effectiveness and also indicate that implicit features of data sets can be revealed. In the comparison experiments, the proposed method shows its advantage in robustness. |
| first_indexed | 2024-03-09T16:25:11Z |
| format | Article |
| id | doaj.art-0513f2e57fa248dd9f0aaaf12a7a4da5 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T16:25:11Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-0513f2e57fa248dd9f0aaaf12a7a4da52023-11-24T15:08:41ZengMDPI AGSymmetry2073-89942023-10-011511199510.3390/sym15111995Learning by Autonomous Manifold Deformation with an Intrinsic Deforming FieldXiaodong Zhuang0Nikos Mastorakis1Electronics Information College, Qingdao University, Qingdao 266071, ChinaDepartment of Industrial Engineering, Technical University of Sofia, Bulevard Sveti Kliment Ohridski 8, 1000 Sofia, BulgariaA self-organized geometric model is proposed for data dimension reduction to improve the robustness of manifold learning. In the model, a novel mechanism for dimension reduction is presented by the autonomous deforming of data manifolds. The autonomous deforming vector field is proposed to guide the deformation of the data manifold. The flattening of the data manifold is achieved as an emergent behavior under the virtual elastic and repulsive interaction between the data points. The manifold’s topological structure is preserved when it evolves to the shape of lower dimension. The soft neighborhood is proposed to overcome the uneven sampling and neighbor point misjudging problems. The simulation experiment results of data sets prove its effectiveness and also indicate that implicit features of data sets can be revealed. In the comparison experiments, the proposed method shows its advantage in robustness.https://www.mdpi.com/2073-8994/15/11/1995dimension reductionmanifold learningmanifold deformationemergent behaviorfeature extraction |
| spellingShingle | Xiaodong Zhuang Nikos Mastorakis Learning by Autonomous Manifold Deformation with an Intrinsic Deforming Field Symmetry dimension reduction manifold learning manifold deformation emergent behavior feature extraction |
| title | Learning by Autonomous Manifold Deformation with an Intrinsic Deforming Field |
| title_full | Learning by Autonomous Manifold Deformation with an Intrinsic Deforming Field |
| title_fullStr | Learning by Autonomous Manifold Deformation with an Intrinsic Deforming Field |
| title_full_unstemmed | Learning by Autonomous Manifold Deformation with an Intrinsic Deforming Field |
| title_short | Learning by Autonomous Manifold Deformation with an Intrinsic Deforming Field |
| title_sort | learning by autonomous manifold deformation with an intrinsic deforming field |
| topic | dimension reduction manifold learning manifold deformation emergent behavior feature extraction |
| url | https://www.mdpi.com/2073-8994/15/11/1995 |
| work_keys_str_mv | AT xiaodongzhuang learningbyautonomousmanifolddeformationwithanintrinsicdeformingfield AT nikosmastorakis learningbyautonomousmanifolddeformationwithanintrinsicdeformingfield |