Self-adjust Local Connectivity Analysis for Spectral Clustering

Spectral clustering has been applied in various applications. But there still exist some important issues to be resolved, among which the two major ones are to (1) specify the scale parameter in calculating the similarity between data objects, and (2) select propoer eigenvectors to reduce data dimensionality. Though these topics have been studied extensively, the existing methods cannot work well in some complicated scenarios, which limits the wide deployment of the spectral clustering method. In this work, we revisit the above two problems and propose three contributions to the field: 1) a unified framework is designed to study the impact of the scale parameter on similarity between data objects. This framework can easily accommodate various state of art spectral clustering methods in determining the scale parameter; 2) a novel approach based on local connectivity analysis is proposed to specify the scale parameter; 3) propose a new method for eigenvector selection. Compared with existing techniques, the proposed approach has a rigorous theoretical basis and is efficient from practical perspective. Experimental results show the efficacy of our approach to clustering data of different scenarios.