# Modal-set estimation with an application to clustering

arXiv: https://arxiv.org/abs/1606.04166 · HTML: https://mlsanity.com/paper/1606.04166/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jun 2016.

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

- [A Non-Classical Parameterization for Density Estimation Using Sample Moments](https://mlsanity.com/paper/2201.04786/) (2022)
- [How to scale hyperparameters for quickshift image segmentation](https://mlsanity.com/paper/2201.09286/) (2022)
- [TANGO: Clustering with Typicality-Aware Nonlocal Mode-Seeking and Graph-Cut Optimization](https://mlsanity.com/paper/2408.10084/) (2024)

## Abstract (arXiv)

We present a first procedure that can estimate -- with statistical consistency guarantees -- any local-maxima of a density, under benign distributional conditions. The procedure estimates all such local maxima, or textitmodal-sets, of any bounded shape or dimension, including usual point-modes. In practice, modal-sets can arise as dense low-dimensional structures in noisy data, and more generally serve to better model the rich variety of locally-high-density structures in data. The procedure is then shown to be competitive on clustering applications, and moreover is quite stable to a wide range of settings of its tuning parameter.