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

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.

局部众数集与密度脊线是数据生成分布的重要概括性特征。本研究聚焦于从由两个及以上欧几里得空间和/或方向度量空间构成的乘积空间（product space）的点云数据中，估计局部众数与密度脊线。具体而言，我们的方法将（子空间约束）均值漂移算法（mean shift algorithm）拓展至此类乘积空间，以应对泛化过程中潜在的挑战。我们证明了所提方法的算法收敛性，并给出了实用的实现指南。在模拟数据集与真实世界数据集上开展的实验验证了所提方法的有效性。本文的补充材料可在线获取。