Multi-Frequency Vector Diffusion Maps

Yifeng Fan, Zhizhen Zhao
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:1843-1852, 2019.

Abstract

We introduce multi-frequency vector diffusion maps (MFVDM), a new framework for organizing and analyzing high dimensional data sets. The new method is a mathematical and algorithmic generalization of vector diffusion maps (VDM) and other non-linear dimensionality reduction methods. The idea of MFVDM is to incorporates multiple unitary irreducible representations of the alignment group which introduces robustness to noise. We illustrate the efficacy of MFVDM on synthetic and cryo-EM image datasets, achieving better nearest neighbors search and alignment estimation than other baselines as VDM and diffusion maps (DM), especially on extremely noisy data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-fan19a, title = {Multi-Frequency Vector Diffusion Maps}, author = {Fan, Yifeng and Zhao, Zhizhen}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {1843--1852}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/fan19a/fan19a.pdf}, url = {https://proceedings.mlr.press/v97/fan19a.html}, abstract = {We introduce multi-frequency vector diffusion maps (MFVDM), a new framework for organizing and analyzing high dimensional data sets. The new method is a mathematical and algorithmic generalization of vector diffusion maps (VDM) and other non-linear dimensionality reduction methods. The idea of MFVDM is to incorporates multiple unitary irreducible representations of the alignment group which introduces robustness to noise. We illustrate the efficacy of MFVDM on synthetic and cryo-EM image datasets, achieving better nearest neighbors search and alignment estimation than other baselines as VDM and diffusion maps (DM), especially on extremely noisy data.} }
Endnote
%0 Conference Paper %T Multi-Frequency Vector Diffusion Maps %A Yifeng Fan %A Zhizhen Zhao %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-fan19a %I PMLR %P 1843--1852 %U https://proceedings.mlr.press/v97/fan19a.html %V 97 %X We introduce multi-frequency vector diffusion maps (MFVDM), a new framework for organizing and analyzing high dimensional data sets. The new method is a mathematical and algorithmic generalization of vector diffusion maps (VDM) and other non-linear dimensionality reduction methods. The idea of MFVDM is to incorporates multiple unitary irreducible representations of the alignment group which introduces robustness to noise. We illustrate the efficacy of MFVDM on synthetic and cryo-EM image datasets, achieving better nearest neighbors search and alignment estimation than other baselines as VDM and diffusion maps (DM), especially on extremely noisy data.
APA
Fan, Y. & Zhao, Z.. (2019). Multi-Frequency Vector Diffusion Maps. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:1843-1852 Available from https://proceedings.mlr.press/v97/fan19a.html.

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