# Algorithms for ridge estimation with convergence guarantees

arXiv: https://arxiv.org/abs/2104.12314 · HTML: https://mlsanity.com/paper/2104.12314/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 61 references that are in the map.
- First posted on arXiv 26 Apr 2021.

## Builds on (most cited first, 1 of 1)

- [Asymptotic theory for density ridges](https://mlsanity.com/paper/1406.5663/) (2014)

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

- [Mode and Ridge Estimation in Euclidean and Directional Product Spaces: A Mean Shift Approach](https://mlsanity.com/paper/2110.08505/) (2021)
- [Statistical embedding: Beyond principal components](https://mlsanity.com/paper/2106.01858/) (2021)
- [EM Approaches to Nonparametric Estimation for Mixture of Linear Regressions](https://mlsanity.com/paper/2510.14890/) (2025)
- [Stable Density Ridges: Consistency and Convergence of Subspace Constrained Mean Shift](https://mlsanity.com/paper/2608.05112/) (2026)

## Abstract (arXiv)

The extraction of filamentary structure from a point cloud is discussed. The filaments are modeled as ridge lines or higher dimensional ridges of an underlying density. We propose two novel algorithms, and provide theoretical guarantees for their convergences, by which we mean that the algorithms can asymptotically recover the full ridge set. We consider the new algorithms as alternatives to the Subspace Constrained Mean Shift (SCMS) algorithm for which no such theoretical guarantees are known.