On Spectral Analysis of Directed Signed Graphs

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It has been shown that the adjacency eigenspace of a network contains key information of its underlying structure. However, there has been no study on spectral analysis of the adjacency matrices of directed signed graphs. In this paper, we derive theoretical approximations of spectral projections from such directed signed networks using matrix perturbation theory. We use the derived theoretical results to study the influences of negative intra cluster and inter cluster directed edges on node spectral projections. We then develop a spectral clustering based graph partition algorithm, SC-DSG, and conduct evaluations on both synthetic and real datasets. Both theoretical analysis and empirical evaluation demonstrate the effectiveness of the proposed algorithm.


Principal Investigator: Xintao Wu

Acknowledgements: The authors would like to thank anonymous reviewers for their valuable comments and suggestions. This work was supported in part by U.S. National Science Foundation under awards (1564039 and 1564250).