Non-traditional spectral clustering algorithms for the detection of community structure in complex networks: a comparative analysis

The detection of community structure in complex networks is crucial since it provides insight into the substructures of the whole network. Spectral clustering algorithms that employ the eigenvalues and eigenvectors of an appropriate input matrix have been successfully applied in this field. Despite its empirical success in community detection, spectral clustering has been criticized for its inefficiency when dealing with large scale data sets. This is confirmed by the fact that the time complexity for spectral clustering is cubic with respect to the number of instances; even the memory efficient iterative eigensolvers, such as the power method, may converge slowly to the desired solutions. In efforts to improve the complexity and performance, many non-traditional spectral clustering algorithms have been proposed. Rather than using the real eigenvalues and eigenvectors as in the traditional methods, the non-traditional clusterings employ additional topological structure information characterized by the spectrum of a matrix associated with the network involved, such as the complex eigenvalues and their corresponding complex eigenvectors, eigenspaces and semi-supervised labels. However, to the best of our knowledge, no work has been devoted to comparison among these newly developed approaches. This is the main goal of this paper, through evaluating the effectiveness of these spectral algorithms against some benchmark networks. The experimental results demonstrate that the spectral algorithm based on the eigenspaces achieves the best performance but is the slowest algorithm; the semi-supervised spectral algorithm is the fastest but its performance largely depends on the prior knowledge; and the spectral method based on the complement network shows similar performance to the conventional ones.