# Accelerate Vector Diffusion Maps by Landmarks

arXiv: https://arxiv.org/abs/2603.21247 · HTML: https://mlsanity.com/paper/2603.21247/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 25 references that are in the map.
- First posted on arXiv 22 Mar 2026.

## Builds on (most cited first, 8 of 8)

- [Spectral Convergence of the connection Laplacian from random samples](https://mlsanity.com/paper/1306.1587/) (2013)
- [Rotationally Invariant Image Representation for Viewing Direction Classification in Cryo-EM](https://mlsanity.com/paper/1309.7643/) (2013)
- [Latent common manifold learning with alternating diffusion: analysis and applications](https://mlsanity.com/paper/1602.00078/) (2016)
- [Solving Jigsaw Puzzles By the Graph Connection Laplacian](https://mlsanity.com/paper/1811.03188/) (2018)
- [Alternating Projection, Ptychographic Imaging and Phase Synchronization](https://mlsanity.com/paper/1402.0550/) (2014)
- [Cohomology of Cryo-Electron Microscopy](https://mlsanity.com/paper/1604.01319/) (2016)
- [Unsupervised Ensembling of Multiple Software Sensors with Phase Synchronization: A Robust Approach For Electrocardiogram-derived Respiration](https://mlsanity.com/paper/2006.13054/) (2020)
- [Landmark Alternating Diffusion](https://mlsanity.com/paper/2404.19649/) (2024)

## Abstract (arXiv)

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.