Coarse-refinement dilemma: On generalization bounds for data clustering

作者：

Highlights：

• Topological definition of the data clustering and hierarchical clustering.

• Presentation and demonstration of the Coarse-Refinement Dilemma.

• Presentation of homology consistency based on multidimensional persistent homology.

• Formulation of generalization bounds for homology consistency.

摘要

•Topological definition of the data clustering and hierarchical clustering.•Presentation and demonstration of the Coarse-Refinement Dilemma.•Presentation of homology consistency based on multidimensional persistent homology.•Formulation of generalization bounds for homology consistency.

论文关键词：Data clustering,Topology,Persistent homology,Multidimensional persistence,Algorithm stability

论文评审过程：Received 14 November 2019, Revised 10 April 2021, Accepted 8 June 2021, Available online 6 July 2021, Version of Record 19 July 2021.

论文官网地址：https://doi.org/10.1016/j.eswa.2021.115399