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arXiv · 2603.21247

Accelerate Vector Diffusion Maps by Landmarks

Sing-Yuan Yeh·Yi-An Wu·Hau-Tieng Wu·Mao-Pei Tsui
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Abstract

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.

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Sing-Yuan Yeh, Yi-An Wu, Hau-Tieng Wu, Mao-Pei Tsui. 2026-08-30. Accelerate Vector Diffusion Maps by Landmarks. https://arxiv.org/abs/2603.21247

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