Data Science
H. Hajibabaei; V. Seydi; A. Koochari
Abstract
Background and Objectives: The detection of community in networks is an important tool for revealing hidden data in network analysis. One of the signs that the community exists in the network is the neighborhood density between nodes. Also, the existence of a concept called a motif indicates that a community ...
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Background and Objectives: The detection of community in networks is an important tool for revealing hidden data in network analysis. One of the signs that the community exists in the network is the neighborhood density between nodes. Also, the existence of a concept called a motif indicates that a community with a high edge density has a correlation between nodes that go beyond their close neighbors. Motifs are repetitive edge patterns that are frequently seen in the network.Methods: By estimating the triangular motif in the network, our proposed probabilistic motif-based community detection model (PMCD) helps to find the communities in the network. The idea of the proposed model is network analysis based on structural density between nodes and detecting communities by estimating motifs using probabilistic methods.Results: The suggested model's output is the strength of each node's affiliation to the communities and detecting overlaps in communities. To evaluate the performance and accuracy of the proposed method, experiments are done on real-world and synthetic networks. The findings show that, compared to other algorithms, the proposed method is acting more accurately and densely in detecting communities.Conclusion: The advantage of PMCD in using the probabilistic generative model is speeding up the computation of the hidden parameters and establishing the community based on the likelihood of triangular motifs. In fact, the proposed method proves there is a probabilistic correlation between the observation of two node pairs in different communities and the increased existence of motif structure in the network.
Graph Clustering
M. Ghadirian; N. Bigdeli
Abstract
Background and Objectives: Community detection is a critical problem in investigating complex networks. Community detection based on modularity/general modularity density are the popular methods with the advantage of using complex network features and the disadvantage of being NP-hard ...
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Background and Objectives: Community detection is a critical problem in investigating complex networks. Community detection based on modularity/general modularity density are the popular methods with the advantage of using complex network features and the disadvantage of being NP-hard problem for clustering. Moreover, Non-negative matrix factorization (NMF)-based community detection methods are a family of community detection tools that utilize network topology; but most of them cannot thoroughly exploit network features. In this paper, a hybrid NMF-based community detection infrastructure is developed, including modularity/ general modularity density as more comprehensive indices of networks. The proposed infrastructure enables to solve the challenges of combining the NMF method with modularity/general modularity density criteria and improves the community detection methods for complex networks.Methods: First, new representations, similar to the model of symmetric NMF, are derived for the model of community detection based on modularity/general modularity density. Next, these indices are innovatively augmented to the proposed hybrid NMF-based model as two novel models called ‘general modularity density NMF (GMDNMF) and mixed modularity NMF (MMNMF)’. In order to solve these two NP-hard problems, two iterative optimization algorithms are developed.Results: it is proved that the modularity/general modularity density-based community detection can be consistently represented in the form of SNMF-based community detection. The performances of the proposed models are verified on various artificial and real-world networks of different sizes. It is shown that MMNMF and GMDNMF models outperform other community detection methods. Moreover, the GMDNMF model has better performance with higher computational complexity compared to the MMNMF model.Conclusion: The results show that the proposed MMNMF model improves the performance of community detection based on NMF by employing the modularity index as a network feature for the NMF model, and the proposed GMDNMF model enhances NMF-based community detection by using the general modularity density index.
