Mode and Ridge Estimation in Euclidean and Directional Product Spaces: A Mean Shift Approach
This work addresses a domain-specific problem for researchers in data analysis and machine learning dealing with complex geometric data, but it is incremental as it builds on existing mean shift methods.
The authors tackled the problem of estimating local modes and density ridges from point cloud data in product spaces combining Euclidean and directional metric spaces by extending the mean shift algorithm, demonstrating effectiveness in experiments.
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.