Phase transitions in semisupervised clustering of sparse networks

作者：Zhang Pan^*; Moore Cristopher; Zdeborova Lenka

来源：Physical Review E, 2014, 90(5): 052802.

DOI：10.1103/PhysRevE.90.052802

Predicting labels of nodes in a network, such as community memberships or demographic variables, is an important problem with applications in social and biological networks. A recently discovered phase transition puts fundamental limits on the accuracy of these predictions if we have access only to the network topology. However, if we know the correct labels of some fraction a of the nodes, we can do better. We study the phase diagram of this semisupervised learning problem for networks generated by the stochastic block model. We use the cavity method and the associated belief propagation algorithm to study what accuracy can be achieved as a function of a. For k = 2 groups, we find that the detectability transition disappears for any alpha > 0, in agreement with previous work. For larger k where a hard but detectable regime exists, we find that the easy/hard transition (the point at which efficient algorithms can do better than chance) becomes a line of transitions where the accuracy jumps discontinuously at a critical value of alpha. This line ends in a critical point with a second-order transition, beyond which the accuracy is a continuous function of alpha. We demonstrate qualitatively similar transitions in two real-world networks.

• 出版日期2014-11-5
• 单位中国地震局