Mode and Ridge Estimation in Euclidean and Directional Product Spaces: A Mean Shift Approach
Year: 2025
Type: article
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. Supplementary materials for this article are available online.
Authors: Yikun Zhang, Yen-Chi Chen
Institution: University of Washington
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funders: National Science Foundation, Smithsonian Institution, U.S. Department of Energy, Alfred P. Sloan Foundation, Yale University, Carnegie Institution of Washington, Vanderbilt University, Ohio State University, University of Utah, University of Washington, Johns Hopkins University, Carnegie Mellon University, University of Notre Dame, University of Portsmouth, New Mexico State University, York University, University of Oxford, Ministério da Ciência, Tecnologia e Inovação, Universidad Nacional Autónoma de México, Max-Planck-Institut für Astrophysik, Max-Planck-Institut für Astronomie, Instituto de Astrofísica de Canarias, National Institutes of Health, Office of Science, University of Colorado Boulder, Center for High Performance Computing, Leibniz-Gemeinschaft, National Institute on Aging, Lawrence Berkeley National Laboratory
Awards: Novel Missing Data Approaches for Corrupted Longitudinal Data, G2190936067, G4658249000, CAREER: Inference with graphs: density skeleton and Markov missing graph, National Alzheimer's Coordinating Center, Semiparametric Efficient and Robust Inference on High-Dimensional Data, G9000082286, G9000285695
OpenAlex ID: W4410495144