# Geometric Inference on Kernel Density Estimates

arXiv: https://arxiv.org/abs/1307.7760 · HTML: https://mlsanity.com/paper/1307.7760/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jul 2013.

## Built on by (most cited first, 2 of 2)

- [No Dimensional Sampling Coresets for Classification](https://mlsanity.com/paper/2402.05280/) (2024)
- [Dimensionality Reduction for General KDE Mode Finding](https://mlsanity.com/paper/2305.18755/) (2023)

## Abstract (arXiv)

We show that geometric inference of a point cloud can be calculated by examining its kernel density estimate with a Gaussian kernel. This allows one to consider kernel density estimates, which are robust to spatial noise, subsampling, and approximate computation in comparison to raw point sets. This is achieved by examining the sublevel sets of the kernel distance, which isomorphically map to superlevel sets of the kernel density estimate. We prove new properties about the kernel distance, demonstrating stability results and allowing it to inherit reconstruction results from recent advances in distance-based topological reconstruction. Moreover, we provide an algorithm to estimate its topology using weighted Vietoris-Rips complexes.