# A fully data-driven method for estimating the shape of a point cloud

arXiv: https://arxiv.org/abs/1404.7397 · HTML: https://mlsanity.com/paper/1404.7397/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Apr 2014.

## Built on by (most cited first, 1 of 1)

- [A Simple and Efficient Sampling-based Algorithm for General Reachability Analysis](https://mlsanity.com/paper/2112.05745/) (2021)

## Abstract (arXiv)

Given a random sample of points from some unknown distribution, we propose a new data-driven method for estimating its probability support S. Under the mild assumption that S is r-convex, the smallest r-convex set which contains the sample points is the natural estimator. The main problem for using this estimator in practice is that r is an unknown geometric characteristic of the set S. A stochastic algorithm is proposed for selecting it from the data under the hypothesis that the sample is uniformly generated. The new data-driven reconstruction of S is able to achieve the same convergence rates as the convex hull for estimating convex sets, but under a much more flexible smoothness shape condition. The practical performance of the estimator is illustrated through a real data example and a simulation study.