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.
Cite
@article{arxiv.2603.21247,
title = {Accelerate Vector Diffusion Maps by Landmarks},
author = {Sing-Yuan Yeh and Yi-An Wu and Hau-Tieng Wu and Mao-Pei Tsui},
journal= {arXiv preprint arXiv:2603.21247},
year = {2026}
}