Log-concave Ridge Estimation

TL;DR

This paper introduces a new density ridge estimation algorithm based on a novel definition involving conditional variance, demonstrating advantages over existing methods through simulations and galaxy filament estimation.

Contribution

The paper proposes a new density ridge search algorithm using a conditional variance matrix, offering improvements over the subspace constraint mean shift method.

Findings

The new algorithm outperforms existing methods in simulations.

It successfully estimates galaxy filaments from real survey data.

Demonstrates advantages in accuracy and robustness.

Abstract

We develop a density ridge search algorithm based on a novel density ridge definition. This definition is based on a conditional variance matrix and the mode in the lower dimensional subspace. It is compared to the subspace constraint mean shift algorithm, based on the gradient and Hessian of the underlying probability density function. We show the advantages of the new algorithm in a simulation study and estimate galaxy filaments from a data set of the Baryon Oscillation Spectroscopic Survey.