Asymptotic theory of geometric and adaptive k-means clustering
几何与自适应 k 均值聚类的渐近理论
We revisit Pollard’s classical result on consistency for k-means clustering in Euclidean space, with a focus on extensions in two directions: first, to problems where the data may come from interesting geometric settings (e.g., Riemannian manifolds, reflexive Banach spaces or the Wasserstein space); second, to problems where some parameters are chosen adaptively from the data (e.g., k-medoids or elbow-method k-means). Toward this end, we provide a general theory, which shows…