# Multi-Frequency Vector Diffusion Maps

arXiv: https://arxiv.org/abs/1906.02605 · HTML: https://mlsanity.com/paper/1906.02605/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2019.

## Built on by (most cited first, 4 of 4)

- [Joint Community Detection and Rotational Synchronization via Semidefinite Programming](https://mlsanity.com/paper/2105.06031/) (2021)
- [A Spectral Method for Joint Community Detection and Orthogonal Group Synchronization](https://mlsanity.com/paper/2112.13199/) (2021)
- [Non-Convex Joint Community Detection and Group Synchronization via Generalized Power Method](https://mlsanity.com/paper/2112.14204/) (2021)
- [G-invariant diffusion maps](https://mlsanity.com/paper/2306.07350/) (2023)

## Abstract (arXiv)

We introduce multi-frequency vector diffusion maps (MFVDM), a new framework for organizing and analyzing high dimensional datasets. The new method is a mathematical and algorithmic generalization of vector diffusion maps (VDM) and other non-linear dimensionality reduction methods. MFVDM combines different nonlinear embeddings of the data points defined with multiple unitary irreducible representations of the alignment group that connect two nodes in the graph. We illustrate the efficacy of MFVDM on synthetic data generated according to a random graph model and cryo-electron microscopy image dataset. The new method achieves better nearest neighbor search and alignment estimation than the state-of-the-arts VDM and diffusion maps (DM) on extremely noisy data.