# Generalized Mode and Ridge Estimation

arXiv: https://arxiv.org/abs/1406.1803 · HTML: https://mlsanity.com/paper/1406.1803/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2014.

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

- [Regularization of Mixture Models for Robust Principal Graph Learning](https://mlsanity.com/paper/2106.09035/) (2021)
- [Mode and Ridge Estimation in Euclidean and Directional Product Spaces: A Mean Shift Approach](https://mlsanity.com/paper/2110.08505/) (2021)

## Abstract (arXiv)

The generalized density is a product of a density function and a weight function. For example, the average local brightness of an astronomical image is the probability of finding a galaxy times the mean brightness of the galaxy. We propose a method for studying the geometric structure of generalized densities. In particular, we show how to find the modes and ridges of a generalized density function using a modification of the mean shift algorithm and its variant, subspace constrained mean shift. Our method can be used to perform clustering and to calculate a measure of connectivity between clusters. We establish consistency and rates of convergence for our estimator and apply the methods to data from two astronomical problems.