Adapting Stochastic Block Models to Power-Law Degree Distributions
This addresses a limitation in network modeling for researchers analyzing complex real-world networks, but it is an incremental improvement over existing SBMs.
The authors tackled the problem that stochastic block models (SBMs) cannot handle power-law degree distributions in real-world networks by proposing a new variant called PLD-SBM, which improved cluster prediction accuracies on synthetic and real datasets like Adolescent Health Data and the political blogs network.
Stochastic block models (SBMs) have been playing an important role in modeling clusters or community structures of network data. But, it is incapable of handling several complex features ubiquitously exhibited in real-world networks, one of which is the power-law degree characteristic. To this end, we propose a new variant of SBM, termed power-law degree SBM (PLD-SBM), by introducing degree decay variables to explicitly encode the varying degree distribution over all nodes. With an exponential prior, it is proved that PLD-SBM approximately preserves the scale-free feature in real networks. In addition, from the inference of variational E-Step, PLD-SBM is indeed to correct the bias inherited in SBM with the introduced degree decay factors. Furthermore, experiments conducted on both synthetic networks and two real-world datasets including Adolescent Health Data and the political blogs network verify the effectiveness of the proposed model in terms of cluster prediction accuracies.