Accelerate Vector Diffusion Maps by Landmarks

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.

Machine Learning (stat.ML); Machine Learning (cs.LG); Differential Geometry (math.DG); Data Analysis, Statistics and Probability (physics.data-an)

arXiv:2603.21247 [stat.ML]

(or arXiv:2603.21247v2 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2603.21247 Focus to learn more arXiv-issued DOI via DataCite

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