[2603.21247] Accelerate Vector Diffusion Maps by Landmarks

Statistics > Machine Learning arXiv:2603.21247 (stat) [Submitted on 22 Mar 2026] Title:Accelerate Vector Diffusion Maps by Landmarks Authors:Sing-Yuan Yeh, Yi-An Wu, Hau-Tieng Wu, Mao-Pei Tsui View a PDF of the paper titled Accelerate Vector Diffusion Maps by Landmarks, by Sing-Yuan Yeh and 3 other authors View PDF HTML (experimental) 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. Subjects: Machine Learning (stat.ML); Machine Learning (cs.LG); Differential Geometry (math.DG); Data Analysis, Statistics and Probability (physics.data-an) MSC classes: 58J50, 53C05, 53C21, 62M15, 57R40, 57M50 Cite as: arXiv:2603.21247 [stat.ML]   (or arXiv:2603.21247v1 [stat.ML] for this version)   https://doi.org/10.48550/arXiv.2603....