Phase Transitions in Spectral Community Detection of Large Noisy Networks
This provides theoretical insights into the fundamental limits of community detection algorithms for researchers in network science and machine learning, though it appears incremental to existing phase transition literature.
The paper studies spectral clustering for community detection in networks with Erdos-Renyi noise, proving phase transitions where performance shifts from near-perfect to low detectability as inter-community edge probability exceeds a critical threshold, with bounds derived and validated through simulations.
In this paper, we study the sensitivity of the spectral clustering based community detection algorithm subject to a Erdos-Renyi type random noise model. We prove phase transitions in community detectability as a function of the external edge connection probability and the noisy edge presence probability under a general network model where two arbitrarily connected communities are interconnected by random external edges. Specifically, the community detection performance transitions from almost perfect detectability to low detectability as the inter-community edge connection probability exceeds some critical value. We derive upper and lower bounds on the critical value and show that the bounds are identical when the two communities have the same size. The phase transition results are validated using network simulations. Using the derived expressions for the phase transition threshold we propose a method for estimating this threshold from observed data.