Accelerate Vector Diffusion Maps by Landmarks
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866908905730211840 |
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| author | Yeh, Sing-Yuan Wu, Yi-An Wu, Hau-Tieng Tsui, Mao-Pei |
| author_facet | Yeh, Sing-Yuan Wu, Yi-An Wu, Hau-Tieng Tsui, Mao-Pei |
| contents | We propose a landmark-constrained algorithm, LA-VDM (Landmark Accelerated Vector Diffusion Maps), to accelerate the Vector Diffusion Maps (VDM) framework built upon the Graph Connection Laplacian (GCL), which captures pairwise connection relationships within complex datasets. LA-VDM introduces a novel two-stage normalization that effectively address nonuniform sampling densities in both the data and the landmark sets. Under a manifold model with the frame bundle structure, we show that we can accurately recover the parallel transport with landmark-constrained diffusion from a point cloud, and hence asymptotically LA-VDM converges to the connection Laplacian. The performance and accuracy of LA-VDM are demonstrated through experiments on simulated datasets and an application to nonlocal image denoising. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21247 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Accelerate Vector Diffusion Maps by Landmarks Yeh, Sing-Yuan Wu, Yi-An Wu, Hau-Tieng Tsui, Mao-Pei Machine Learning Differential Geometry Data Analysis, Statistics and Probability 58J50, 53C05, 53C21, 62M15, 57R40, 57M50 We propose a landmark-constrained algorithm, LA-VDM (Landmark Accelerated Vector Diffusion Maps), to accelerate the Vector Diffusion Maps (VDM) framework built upon the Graph Connection Laplacian (GCL), which captures pairwise connection relationships within complex datasets. LA-VDM introduces a novel two-stage normalization that effectively address nonuniform sampling densities in both the data and the landmark sets. Under a manifold model with the frame bundle structure, we show that we can accurately recover the parallel transport with landmark-constrained diffusion from a point cloud, and hence asymptotically LA-VDM converges to the connection Laplacian. The performance and accuracy of LA-VDM are demonstrated through experiments on simulated datasets and an application to nonlocal image denoising. |
| title | Accelerate Vector Diffusion Maps by Landmarks |
| topic | Machine Learning Differential Geometry Data Analysis, Statistics and Probability 58J50, 53C05, 53C21, 62M15, 57R40, 57M50 |
| url | https://arxiv.org/abs/2603.21247 |