scholarly journals Algorithm independent bounds on community detection problems and associated transitions in stochastic block model graphs

2014 ◽  
Vol 3 (3) ◽  
pp. 333-360 ◽  
Author(s):  
Richard K. Darst ◽  
David R. Reichman ◽  
Peter Ronhovde ◽  
Zohar Nussinov
Keyword(s):  
Community Detection ◽  
Block Model ◽  
Stochastic Block Model ◽  
Community Detection Problems

scholarly journals Active Learning in the Geometric Block Model

2020 ◽  
Vol 34 (04) ◽  
pp. 3641-3648 ◽  
Author(s):  
Eli Chien ◽  
Antonia Tulino ◽  
Jaime Llorca
Keyword(s):  
Active Learning ◽  
Community Detection ◽  
Random Graphs ◽  
State Of The Art ◽  
Superior Performance ◽  
Model Parameters ◽  
Block Model ◽  
Stochastic Block Model ◽  
Synthetic Datasets ◽  
Community Detection Problems

The geometric block model is a recently proposed generative model for random graphs that is able to capture the inherent geometric properties of many community detection problems, providing more accurate characterizations of practical community structures compared with the popular stochastic block model. Galhotra et al. recently proposed a motif-counting algorithm for unsupervised community detection in the geometric block model that is proved to be near-optimal. They also characterized the regimes of the model parameters for which the proposed algorithm can achieve exact recovery. In this work, we initiate the study of active learning in the geometric block model. That is, we are interested in the problem of exactly recovering the community structure of random graphs following the geometric block model under arbitrary model parameters, by possibly querying the labels of a limited number of chosen nodes. We propose two active learning algorithms that combine the use of motif-counting with two different label query policies. Our main contribution is to show that sampling the labels of a vanishingly small fraction of nodes (sub-linear in the total number of nodes) is sufficient to achieve exact recovery in the regimes under which the state-of-the-art unsupervised method fails. We validate the superior performance of our algorithms via numerical simulations on both real and synthetic datasets.

scholarly journals Community Detection under Stochastic Block Model Likelihood Optimization via Tabu Search –Fuzzy C-Mean Method for Social Network Data

2020 ◽  
pp. 2695-2704
Author(s):  
Ali Falah Yaqoob ◽  
Basad Al-Sarray
Keyword(s):  
Tabu Search ◽  
Community Detection ◽  
Likelihood Function ◽  
Information Criteria ◽  
Block Model ◽  
Stochastic Block Model ◽  
Biological Studies ◽  
Np Hard Problem ◽  
Tabu Search Method ◽  
Definition Of

     Structure of network, which is known as community detection in networks, has received a great attention in diverse topics, including social sciences, biological studies, politics, etc. There are a large number of studies and practical approaches that were designed to solve the problem of finding the structure of the network. The definition of complex network model based on clustering is a non-deterministic polynomial-time hardness (NP-hard) problem. There are no ideal techniques to define the clustering. Here, we present a statistical approach based on using the likelihood function of a Stochastic Block Model (SBM). The objective is to define the general model and select the best model with high quality. Therefore, integrating the Tabu Search method with Fuzzy c-Mean (FCM) is implemented in different settings. The experiments are designed to find the best structure for different types of networks by maximizing the objective functions. SBM selections are computed by applying two types of criteria, namely Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC). The results show the ability of the proposed method to find the best community of the given networks.

scholarly journals Eigenvalues of the non-backtracking operator detached from the bulk

2020 ◽  
pp. 2150028
Author(s):  
Simon Coste ◽  
Yizhe Zhu
Keyword(s):  
Information Processing ◽  
Community Detection ◽  
Eigenvalue Problems ◽  
Real Eigenvalue ◽  
Block Model ◽  
Stochastic Block Model ◽  
Neural Information ◽  
Neural Information Processing ◽  
Quadratic Eigenvalue Problems ◽  
Quadratic Eigenvalue

We describe the non-backtracking spectrum of a stochastic block model with connection probabilities [Formula: see text]. In this regime we answer a question posed in [L. Dall’Amico, R. Couillet and N. Tremblay, Revisiting the Bethe–Hessian: Improved community detection in sparse heterogeneous graphs, in Advances in Neural Information Processing Systems (2019), pp. 4039–4049] regarding the existence of a real eigenvalue “inside” the bulk, close to the location [Formula: see text]. We also introduce a variant of the Bauer–Fike theorem well suited for perturbations of quadratic eigenvalue problems, which could be of independent interest.

scholarly journals Community Detection in Networks Based on Modified PageRank and Stochastic Block Model

IEEE Access ◽  
2018 ◽  
Vol 6 ◽  
pp. 77133-77144 ◽  
Author(s):  
Jing Chen ◽  
Guangluan Xu ◽  
Yang Wang ◽  
Yuanben Zhang ◽  
Lei Wang ◽  
...  
Keyword(s):  
Community Detection ◽  
Block Model ◽  
Stochastic Block Model
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