Diffusion K-means clustering on manifolds: Provable exact recovery via semidefinite relaxations

نویسندگان

چکیده

We introduce the diffusion K-means clustering method on Riemannian submanifolds, which maximizes within-cluster connectedness based distance. The constructs a random walk similarity graph with vertices as data points randomly sampled manifolds and edges similarities given by kernel that captures local geometry of manifolds. is multi-scale tool suitable for non-linear non-Euclidean geometric features in mixed dimensions. Given number clusters, we propose polynomial-time convex relaxation algorithm via semidefinite programming (SDP) to solve K-means. In addition, also nuclear norm regularized SDP adaptive clusters. both cases, show exact recovery SDPs can be achieved under between-cluster separability together quantify hardness manifold problem. further localized using bandwidth estimated from nearest neighbors. fully probability density structures underlying submanifolds.

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ژورنال

عنوان ژورنال: Applied and Computational Harmonic Analysis

سال: 2021

ISSN: ['1096-603X', '1063-5203']

DOI: https://doi.org/10.1016/j.acha.2020.03.002