Spectral Clustering for Large-Scale Social Networks via a Pre-Coarsening Sampling based NystrÖm Method

Spectral clustering has exhibited a superior performance in analyzing the cluster structure of network. However, the exponentially computational complexity limits its application in analyzing large-scale social networks. To tackle this problem, many low-rank matrix approximating algorithms are proposed, of which the NystrOm method is an approach with proved lower approximate errors. Currently, most existing sampling techniques for NystrOm method are designed on affinity matrices, which are time-consuming to compute by some similarity metrics. Moreover, the social networks are often built on link relations, in which there is no information to construct an affinity matrix for the approximate computing of NystrOm method for spectral clustering except for the degrees of nodes. This paper proposes a spectral clustering algorithm for large-scale social networks via a pre-coarsening sampling based NystrOm method. By virtue of a novel triangle-based coarsening policy, the proposed algorithm first shrinks the social network into a smaller weighted network, and then does an efficient sampling for NystrOm method to approximate the eigen-decomposition of matrix of spectral clustering. Experimental results on real large-scale social networks demonstrate that the proposed algorithm outperforms the state-of-the-art spectral clustering algorithms, which are realized by the existing sampling techniques based NystrOm methods.