  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.
