Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2014-11-01

Journal: SCIENCE CHINA-INFORMATION SCIENCES

Included Journals: Scopus、EI、SCIE

Volume: 57

Issue: 11

Page Number: 1-17

ISSN: 1674-733X

Key Words: spectral clustering method; normalized Laplacian matrices; eigenvalue; eigenspace; matrix perturbation theory

Abstract: In this paper, we present a perturbation analysis for the matrices in the multiway normalized cut spectral clustering method based on the matrix perturbation theory. The analytical results show that the eigenvalues and the eigenspaces of the normalized Laplacian matrices are continuous. Therefore, clustering algorithms can be designed according to the special properties of the normalized Laplacian matrices in the ideal case and the method can be extended to the general case based on the continuity of the eigenvalues and the eigenspaces of the normalized Laplacian matrices. The numerical results are consistent with the theoretical results.