# Probabilistic smallest enclosing ball in high dimensions via subgradient sampling

arXiv: https://arxiv.org/abs/1902.10966 · HTML: https://mlsanity.com/paper/1902.10966/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Feb 2019.

## Built on by (most cited first, 4 of 4)

- [Improved Learning via k-DTW: A Novel Dissimilarity Measure for Curves](https://mlsanity.com/paper/2505.23431/) (2025)
- [Horoballs and the subgradient method](https://mlsanity.com/paper/2403.15749/) (2024)
- [Hardness of High-Dimensional Linear Classification](https://mlsanity.com/paper/2603.19061/) (2026)
- [An Efficient Variant of One-Class SVM with Lifelong Online Learning Guarantees](https://mlsanity.com/paper/2512.11052/) (2025)

## Abstract (arXiv)

We study a variant of the median problem for a collection of point sets in high dimensions. This generalizes the geometric median as well as the (probabilistic) smallest enclosing ball (pSEB) problems. Our main objective and motivation is to improve the previously best algorithm for the pSEB problem by reducing its exponential dependence on the dimension to linear. This is achieved via a novel combination of sampling techniques for clustering problems in metric spaces with the framework of stochastic subgradient descent. As a result, the algorithm becomes applicable to shape fitting problems in Hilbert spaces of unbounded dimension via kernel functions. We present an exemplary application by extending the support vector data description (SVDD) shape fitting method to the probabilistic case. This is done by simulating the pSEB algorithm implicitly in the feature space induced by the kernel function.