Python code to reproduce the experimental evaluation of the algorithms proposed in the NeurIPS 2022 publication "Approximate Euclidean lengths and distances beyond Johnson-Lindenstrauss". If you download or use this code for research purposes please cite the corresponding publication:
@inproceedings{
sobczyk2022approximate,
title={Approximate Euclidean lengths and distances beyond Johnson-Lindenstrauss},
author={Aleksandros Sobczyk and Mathieu Luisier},
booktitle={Advances in Neural Information Processing Systems},
editor={Alice H. Oh and Alekh Agarwal and Danielle Belgrave and Kyunghyun Cho},
year={2022},
url={https://openreview.net/forum?id=_N4k45mtnuq}
}
The Python package and the exeutable script can be installed directly with pip:
pip install git+https://github.com/IBM/JLPlusPlus
An executable script, compare-jl-vs-jlpp, is installed along with the package, which compare the approximation accuracy of the proposed algorithms with standard Johnson-Lindenstrauss approximations.
Several options can be configured by passing the corresponding arguments arguments:
compare-jl-vs-jlpp --help
Usage: compare-jl-vs-jlpp [OPTIONS]
Options:
--n INTEGER RANGE Size of the matrix. [x>=1]
--c FLOAT RANGE Decay factor for the singular values of the
matrix. The i-th singular value is equal to
i^(-c). [x>=0.0]
--rotate BOOLEAN Whether to randonly rotate the column space of
the test matrix or not.
--max-queries INTEGER RANGE Maximum number of matrix-vector queries for
both algorithms, passed to:
np.arange(min_queries, max_queries+1, step)
[x>=1]
--min-queries INTEGER RANGE Minimum number of matrix-vector queries for
both algorithms, passed to:
np.arange(min_queries, max_queries+1, step)
[x>=1]
--step INTEGER RANGE Step between min and max number of queries for
np.arange, passed to: np.arange(min_queries,
max_queries+1, step) [x>=1]
--n-tries INTEGER RANGE Number of random tries per experiment. [x>=1]
--help Show this message and exit.
Running the script will produce a .png image with the convergence comparison of the two methods.
For more details on the algorithms see here.