Multi-frequency vector diffusion maps

Yifeng Fan, Zhizhen Zhao

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish (US)
Title of host publication36th International Conference on Machine Learning, ICML 2019
PublisherInternational Machine Learning Society (IMLS)
Pages3279-3288
Number of pages10
ISBN (Electronic)9781510886988
StatePublished - Jan 1 2019
Event36th International Conference on Machine Learning, ICML 2019 - Long Beach, United States
Duration: Jun 9 2019Jun 15 2019

Publication series

Name36th International Conference on Machine Learning, ICML 2019
Volume2019-June

Conference

Conference36th International Conference on Machine Learning, ICML 2019
CountryUnited States
CityLong Beach
Period6/9/196/15/19

ASJC Scopus subject areas

  • Education
  • Computer Science Applications
  • Human-Computer Interaction

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  • Cite this

    Fan, Y., & Zhao, Z. (2019). Multi-frequency vector diffusion maps. In 36th International Conference on Machine Learning, ICML 2019 (pp. 3279-3288). (36th International Conference on Machine Learning, ICML 2019; Vol. 2019-June). International Machine Learning Society (IMLS).