Mode and Ridge Estimation in Euclidean and Directional Product Spaces: A Mean Shift Approach

Abstract

The set of local modes and density ridge lines are important summary characteristics of the data-generating distribution. In this work, we focus on estimating local modes and density ridges from point cloud data in a product space combining two or more Euclidean and/or directional metric spaces. Specifically, our approach extends the (subspace constrained) mean shift algorithm to such product spaces, addressing potential challenges in the generalization process. We establish the algorithmic convergence of the proposed methods, along with practical implementation guidelines. Experiments on simulated and real-world datasets demonstrate the effectiveness of our proposed methods.

72 pages (22 pages for the main paper), 10 figures, 5 tables. To appear in the Journal of Computational and Graphical Statistics

References in corpus (7)

• Firefly (Fitting IteRativEly For Likelihood analYsis): a full spectral fitting code
• The spin and orientation of dark matter halos within cosmic filaments
• A review of mean-shift algorithms for clustering
• Generalized Mode and Ridge Estimation
• SCONCE: A cosmic web finder for spherical and conic geometries
• The EM Perspective of Directional Mean Shift Algorithm
• Bump hunting through density curvature features