# Statistical Inference using the Morse-Smale Complex

arXiv: https://arxiv.org/abs/1506.08826 · HTML: https://mlsanity.com/paper/1506.08826/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2015.

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

- [Moving Up the Cluster Tree with the Gradient Flow](https://mlsanity.com/paper/2109.08362/) (2021)
- [Clustering by Hill-Climbing: Consistency Results](https://mlsanity.com/paper/2202.09023/) (2022)
- [An Asymptotic Equivalence between the Mean-Shift Algorithm and the Cluster Tree](https://mlsanity.com/paper/2111.10298/) (2021)
- [Stable Density Ridges: Consistency and Convergence of Subspace Constrained Mean Shift](https://mlsanity.com/paper/2608.05112/) (2026)

## Abstract (arXiv)

The Morse-Smale complex of a function f decomposes the sample space into cells where f is increasing or decreasing. When applied to nonparametric density estimation and regression, it provides a way to represent, visualize, and compare multivariate functions. In this paper, we present some statistical results on estimating Morse-Smale complexes. This allows us to derive new results for two existing methods: mode clustering and Morse-Smale regression. We also develop two new methods based on the Morse-Smale complex: a visualization technique for multivariate functions and a two-sample, multivariate hypothesis test.