arXiv Machine Learning By Sing-Yuan Yeh, Yi-An Wu, Hau-Tieng Wu, Mao-Pei Tsui

Accelerate Vector Diffusion Maps by Landmarks

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The paper introduces LA-VDM, a landmark‑constrained algorithm that speeds up Vector Diffusion Maps (VDM) by employing a two‑stage normalization to handle nonuniform sampling in both data and landmark sets. It demonstrates that, under a manifold model with a frame bundle structure, LA‑VDM can accurately recover parallel transport from a point cloud and asymptotically converges to the connection Laplacian. Experiments on simulated data and a nonlocal image denoising application confirm the method’s performance and accuracy.

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