Multi-Frequency Vector Diffusion Maps
This work addresses challenges in dimensionality reduction for noisy datasets, particularly in fields like cryo-electron microscopy, but appears incremental as it builds upon existing vector diffusion maps.
The authors tackled the problem of organizing and analyzing high-dimensional datasets by introducing multi-frequency vector diffusion maps (MFVDM), a generalization of existing methods, and demonstrated its efficacy on synthetic and cryo-electron microscopy data, achieving better nearest neighbor search and alignment estimation than state-of-the-art methods like VDM and diffusion maps on extremely noisy data.
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.