Randomized Dimensionality Reduction for Euclidean Maximization and Diversity Measures
Abstract
Randomized dimensionality reduction is a widely-used algorithmic technique for speeding up large-scale Euclidean optimization problems. In this paper, we study dimension reduction for a variety of maximization problems, including max-matching, max-spanning tree, as well as various measures for dataset diversity. For these problems, we show that the effect of dimension reduction is intimately tied to the doubling dimension $\lambda_X$ of the underlying dataset $X$—a quantity measuring intrinsic dimensionality of point sets. Specifically, the dimension required is $O(\lambda_X)$, which we also show is necessary for some of these problems. This is in contrast to classical dimension reduction results, whose dependence grow with the dataset size $|X|$. We also provide empirical results validating the quality of solutions found in the projected space, as well as speedups due to dimensionality reduction.
Cite
Text
Gao et al. "Randomized Dimensionality Reduction for Euclidean Maximization and Diversity Measures." Proceedings of the 42nd International Conference on Machine Learning, 2025.Markdown
[Gao et al. "Randomized Dimensionality Reduction for Euclidean Maximization and Diversity Measures." Proceedings of the 42nd International Conference on Machine Learning, 2025.](https://mlanthology.org/icml/2025/gao2025icml-randomized/)BibTeX
@inproceedings{gao2025icml-randomized,
title = {{Randomized Dimensionality Reduction for Euclidean Maximization and Diversity Measures}},
author = {Gao, Jie and Jayaram, Rajesh and Kolbe, Benedikt and Sapir, Shay and Schwiegelshohn, Chris and Silwal, Sandeep and Waingarten, Erik},
booktitle = {Proceedings of the 42nd International Conference on Machine Learning},
year = {2025},
pages = {18363-18385},
volume = {267},
url = {https://mlanthology.org/icml/2025/gao2025icml-randomized/}
}