A Spectral Algorithm with Additive Clustering for the Recovery of Overlapping Communities in Networks
This paper presents a novel spectral algorithm with additive clustering, designed to identify overlapping communities in networks. The algorithm is based on geometric properties of the spectrum of the expected adjacency matrix in a random graph model that we call stochastic blockmodel with overlap (SBMO). An adaptive version of the algorithm, that does not require the knowledge of the number of hidden communities, is proved to be consistent under the SBMO when the degrees in the graph are (slightly more than) logarithmic. The algorithm is shown to perform well on simulated data and on real-world graphs with known overlapping communities.
- 3.Arthur, D., Vassilvitskii, S.: k-means++: the advantage of careful seeding. In: Proceedings of the 18th ACM-SIAM Symposium on Discrete Algorithms (2007)Google Scholar
- 9.Mc Auley, J., Leskovec, J.: Learning to discover social circles in ego networks. In: NIPS, vol. 25, pp. 548–556 (2012)Google Scholar
- 16.Yang, J., Leskovec, J.: Community-affiliation graph model for overlapping community detection. In: IEEE International Conference on Data Mining (2012)Google Scholar
- 17.Zelnik-Manor, L., Perona, P.: Self-tuning spectral clustering. In: Advances in Neural Information Processing Systems (2004)Google Scholar
- 19.Zhang, Y., Levina, E., Zhu, J.: Detecting overlapping communities in networks with spectral methods (2014). arXiv:1412.3432v1