Sharp performance bounds for graph clustering via convex optimization

Ramya Korlakai Vinayak, Samet Oymak, Babak Hassibi
2014 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
The problem of finding clusters in a graph arises in several applications such as social networks, data mining and computer networks. A typical, convex optimization-approach, that is often adopted is to identify a sparse plus low-rank decomposition of the adjacency matrix of the graph, with the (dense) low-rank component representing the clusters. In this paper, we sharply characterize the conditions for successfully identifying clusters using this approach. In particular, we introduce the
more » ... ctive density" of a cluster that measures its significance and we find explicit upper and lower bounds on the minimum effective density that demarcates regions of success or failure of this technique. Our conditions are in terms of (a) the size of the clusters, (b) the denseness of the graph, and (c) regularization parameter of the convex program. We also present extensive simulations that corroborate our theoretical findings.
doi:10.1109/icassp.2014.6855219 dblp:conf/icassp/VinayakOH14 fatcat:3z7rkihtejchbgdfjictvugtpe