10 research outputs found
Strong consistency of spectral clustering for stochastic block models
PDF includes supplement with proofs, lemmas and additional simulation results.</p
Cluster-size constrained network partitioning
International audienceIn this paper we consider a graph clustering problem with a given number of clusters and approximate desired sizes of the clusters. One possible motivation for such task could be the problem of databases or servers allocation within several given large computational clusters, where we want related objects to share the same cluster in order to minimize latency and transaction costs. This task differs from the original community detection problem. To solve this task, we adopt some ideas from Glauber Dynamics and Label Propagation Algorithm. At the same time we consider no additional information about node labels, so the task has the nature of unsupervised learning. We propose an algorithm for the problem, show that it works well for a large set of parameters of Stochastic Block Model (SBM) and theoretically show that its running time complexity for achieving almost exact recovery is of O(n·d·ω) for the mean-field SBM with d being the average degree and ω tending to infinity arbitrary slow. Other significant advantage of the proposed approach is its local nature, which means it can be efficiently distributed with no scheduling or synchronization
Degree-corrected distribution-free model for community detection in weighted networks
A degree-corrected distribution-free model is proposed for weighted social
networks with latent structural information. The model extends the previous
distribution-free models by considering variation in node degree to fit
real-world weighted networks, and it also extends the classical
degree-corrected stochastic block model from un-weighted network to weighted
network. We design an algorithm based on the idea of spectral clustering to fit
the model. Theoretical framework on consistent estimation for the algorithm is
developed under the model. Theoretical results when edge weights are generated
from different distributions are analyzed. We also propose a general modularity
as an extension of Newman's modularity from un-weighted network to weighted
network. Using experiments with simulated and real-world networks, we show that
our method significantly outperforms the uncorrected one, and the general
modularity is effective.Comment: 21 pages, 11 figures, 5 tables, comments are welcom