# Space Partitioning and Regression Mode Seeking via a Mean-Shift-Inspired Algorithm

arXiv: https://arxiv.org/abs/2104.10103 · HTML: https://mlsanity.com/paper/2104.10103/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 40 references that are in the map.
- First posted on arXiv 20 Apr 2021.

## Builds on (most cited first, 5 of 5)

- [A Population Background for Nonparametric Density-Based Clustering](https://mlsanity.com/paper/1408.1381/) (2014)
- [A Comprehensive Approach to Mode Clustering](https://mlsanity.com/paper/1406.1780/) (2014)
- [Nonparametric modal regression](https://mlsanity.com/paper/1412.1716/) (2014)
- [Bandwidth selection for nonparametric modal regression](https://mlsanity.com/paper/1711.00177/) (2017)
- [House Price Modeling over Heterogeneous Regions with Hierarchical Spatial Functional Analysis](https://mlsanity.com/paper/1803.00919/) (2018)

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

- [Clustering by Hill-Climbing: Consistency Results](https://mlsanity.com/paper/2202.09023/) (2022)
- [Stable Density Ridges: Consistency and Convergence of Subspace Constrained Mean Shift](https://mlsanity.com/paper/2608.05112/) (2026)

## Abstract (arXiv)

The mean shift (MS) algorithm is a nonparametric method used to cluster sample points and find the local modes of kernel density estimates, using an idea based on iterative gradient ascent. In this paper we develop a mean-shift-inspired algorithm to estimate the modes of regression functions and partition the sample points in the input space. We prove convergence of the sequences generated by the algorithm and derive the non-asymptotic rates of convergence of the estimated local modes for the underlying regression model. We also demonstrate the utility of the algorithm for data-enabled discovery through an application on biomolecular structure data. An extension to subspace constrained mean shift (SCMS) algorithm used to extract ridges of regression functions is briefly discussed.