# Projected support points: a new method for high-dimensional data reduction

arXiv: https://arxiv.org/abs/1708.06897 · HTML: https://mlsanity.com/paper/1708.06897/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Aug 2017.

## Built on by (most cited first, 3 of 3)

- [Compressed Monte Carlo with application in particle filtering](https://mlsanity.com/paper/2107.08459/) (2021)
- [Weighted Support Points from Random Measures: An Interpretable Alternative for Generative Modeling](https://mlsanity.com/paper/2508.21255/) (2025)
- [Stein Kernelized Molecular Dynamics for Active Learning of Interatomic Potentials](https://mlsanity.com/paper/2606.04100/) (2026)

## Abstract (arXiv)

In an era where big and high-dimensional data is readily available, data scientists are inevitably faced with the challenge of reducing this data for expensive downstream computation or analysis. To this end, we present here a new method for reducing high-dimensional big data into a representative point set, called projected support points (PSPs). A key ingredient in our method is the so-called sparsity-inducing (SpIn) kernel, which encourages the preservation of low-dimensional features when reducing high-dimensional data. We begin by introducing a unifying theoretical framework for data reduction, connecting PSPs with fundamental sampling principles from experimental design and Quasi-Monte Carlo. Through this framework, we then derive sparsity conditions under which the curse-of-dimensionality in data reduction can be lifted for our method. Next, we propose two algorithms for one-shot and sequential reduction via PSPs, both of which exploit big data subsampling and majorization-minimization for efficient optimization. Finally, we demonstrate the practical usefulness of PSPs in two real-world applications, the first for data reduction in kernel learning, and the second for reducing Markov Chain Monte Carlo (MCMC) chains.