Dataset for Space Partitioning and Regression Mode Seeking via a Mean-Shift-Inspired Algorithm

The mean shift (MS) algorithm is a nonparametric method used to cluster sample points and find the local modes of kernel density estimates, using an idea based on iterative gradient ascent. In this paper we develop a mean-shift-inspired algorithm to estimate the modes of regression functions and partition the sample points in the input space. We prove convergence of the sequences generated by the algorithm and derive the non-asymptotic rates of convergence of the estimated local modes for the underlying regression model. We also demonstrate the utility of the algorithm for data-enabled discovery through an application on biomolecular structure data. An extension to subspace constrained mean shift (SCMS) algorithm used to extract ridges of regression functions is briefly discussed.均值漂移（Mean Shift，MS）算法是一种非参数方法，可用于对样本点进行聚类并寻找核密度估计的局部众数，其核心思想基于迭代梯度上升。本文提出了一种受均值漂移算法启发的新算法，用于估计回归函数的众数并对输入空间中的样本点进行划分。我们证明了该算法所生成序列的收敛性，并推导了针对基础回归模型的估计局部众数的非渐近收敛速率。此外，我们通过在生物分子结构数据上的应用，验证了该算法在数据驱动发现中的实用性。本文还简要讨论了一种用于提取回归函数脊线的子空间约束均值漂移（Subspace Constrained Mean Shift, SCMS）算法的扩展形式。