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| Title | Residual Net Aspect of Disk stitching-based Manifold Reconstruction Method |
| Creator | 蔡炎龍 Tsai, Yen-Lung;Lin, Tse-Yu |
| Contributor | 應數系 |
| Date | 2024-01 |
| Date Issued | 12-Mar-2025 11:17:21 (UTC+8) |
| Summary | Manifold learning is a branch of nonlinear dimensionality reduction based on the assumption that data of interest lies in a low-dimensional manifold embedded in a higher-dimensional space. The goal of manifold reconstruction is to reconstruct a Riemannian manifold for Euclidean and non-Euclidean datasets. One differential geometry-based framework of manifold reconstruction proposed by Fefferman et al (2020) state a reconstruction process from both of theoretical and computational aspects. Algorithm of this type is called the disk stitching method since multiple tangent affine spaces will be glued smoothly. In this work, we aim to provide a new point of view to rephrase this process as a learning process of a residual neural network model. Each local affine orthogonal projection can be viewed as a residual block satisfying some functional equations. This idea offers a new insight to study the interdisciplinary relationship of differential geometry and deep learning in the future. |
| Relation | 2024 Joint Mathematics Meetings (JMM 2024), AMS (American Mathematical Society) |
| Type | conference |
| dc.contributor | 應數系 | |
| dc.creator (作者) | 蔡炎龍 | |
| dc.creator (作者) | Tsai, Yen-Lung;Lin, Tse-Yu | |
| dc.date (日期) | 2024-01 | |
| dc.date.accessioned | 12-Mar-2025 11:17:21 (UTC+8) | - |
| dc.date.available | 12-Mar-2025 11:17:21 (UTC+8) | - |
| dc.date.issued (上傳時間) | 12-Mar-2025 11:17:21 (UTC+8) | - |
| dc.identifier.uri (URI) | https://nccur.lib.nccu.edu.tw/handle/140.119/156219 | - |
| dc.description.abstract (摘要) | Manifold learning is a branch of nonlinear dimensionality reduction based on the assumption that data of interest lies in a low-dimensional manifold embedded in a higher-dimensional space. The goal of manifold reconstruction is to reconstruct a Riemannian manifold for Euclidean and non-Euclidean datasets. One differential geometry-based framework of manifold reconstruction proposed by Fefferman et al (2020) state a reconstruction process from both of theoretical and computational aspects. Algorithm of this type is called the disk stitching method since multiple tangent affine spaces will be glued smoothly. In this work, we aim to provide a new point of view to rephrase this process as a learning process of a residual neural network model. Each local affine orthogonal projection can be viewed as a residual block satisfying some functional equations. This idea offers a new insight to study the interdisciplinary relationship of differential geometry and deep learning in the future. | |
| dc.format.extent | 128 bytes | - |
| dc.format.mimetype | text/html | - |
| dc.relation (關聯) | 2024 Joint Mathematics Meetings (JMM 2024), AMS (American Mathematical Society) | |
| dc.title (題名) | Residual Net Aspect of Disk stitching-based Manifold Reconstruction Method | |
| dc.type (資料類型) | conference |