Code for "Dimensionality Reduction has Quantifiable Imperfections: Two Geometric Bounds" (NeurIPS 2018)
This repo contains the code for calculating the empirical Wasserstein many-to-one and discontinuity.
example_swissroll_pca.ipynb illustrates how the calculation is done.
Blog post: https://www.borealisai.com/en/blog/dimensionality-reduction-finally-has-quantifiable-imperfections/
bibtex entry:
@inproceedings{lui2018dimensionality,
title={Dimensionality Reduction has Quantifiable Imperfections: Two Geometric Bounds},
author={Lui, Kry and Ding, Gavin Weiguang and Huang, Ruitong and McCann, Robert},
booktitle={Advances in Neural Information Processing Systems},
pages={8462--8472},
year={2018}
}- numpy
- scipy
- pot
- faiss
- scikit-learn (for running the examples)