A Spectral Clustering Approach Based on Modularity Maximization for Community Detection Problem

AbstractQuantum chemistry is interested in calculating ground and excited states of molecular systems by solving the electronic Schrödinger equation. The exact numerical solution of this equation, frequently represented as an eigenvalue problem, remains unfeasible for most molecules and requires approximate methods. In this paper we introduce the use of Quantum Community Detection performed using the D-Wave quantum annealer to reduce the molecular Hamiltonian matrix in Slater determinant basis without chemical knowledge. Given a molecule represented by a matrix of Slater determinants, the connectivity between Slater determinants (as off-diagonal elements) is viewed as a graph adjacency matrix for determining multiple communities based on modularity maximization. A gauge metric based on perturbation theory is used to determine the lowest energy cluster. This cluster or sub-matrix of Slater determinants is used to calculate approximate ground state and excited state energies within chemical accuracy. The details of this method are described along with demonstrating its performance across multiple molecules of interest and bond dissociation cases. These examples provide proof-of-principle results for approximate solution of the electronic structure problem using quantum computing. This approach is general and shows potential to reduce the computational complexity of post-Hartree–Fock methods as future advances in quantum hardware become available.

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Community Detection Problem Based on Polarization Measures: An Application to Twitter: The COVID-19 Case in Spain

Mathematics ◽

10.3390/math9040443 ◽

2021 ◽

Vol 9 (4) ◽

pp. 443

Author(s):

Inmaculada Gutiérrez ◽

Juan Antonio Guevara ◽

Daniel Gómez ◽

Javier Castro ◽

Rosa Espínola

Keyword(s):

Social Networks ◽

Community Detection ◽

Efficient Algorithm ◽

Fuzzy Measure ◽

The Political ◽

Detection Problem ◽

Additional Information ◽

Political Position ◽

Networks Analysis ◽

Polarization Capacity

In this paper, we address one of the most important topics in the field of Social Networks Analysis: the community detection problem with additional information. That additional information is modeled by a fuzzy measure that represents the risk of polarization. Particularly, we are interested in dealing with the problem of taking into account the polarization of nodes in the community detection problem. Adding this type of information to the community detection problem makes it more realistic, as a community is more likely to be defined if the corresponding elements are willing to maintain a peaceful dialogue. The polarization capacity is modeled by a fuzzy measure based on the JDJpol measure of polarization related to two poles. We also present an efficient algorithm for finding groups whose elements are no polarized. Hereafter, we work in a real case. It is a network obtained from Twitter, concerning the political position against the Spanish government taken by several influential users. We analyze how the partitions obtained change when some additional information related to how polarized that society is, is added to the problem.

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Quadratic Program-Based Modularity Maximization for Fuzzy Community Detection in Social Networks

IEEE Transactions on Fuzzy Systems ◽

10.1109/tfuzz.2014.2360723 ◽

2015 ◽

Vol 23 (5) ◽

pp. 1356-1371 ◽

Cited By ~ 18

Author(s):

Jianhai Su ◽

Timothy C. Havens

Keyword(s):

Social Networks ◽

Community Detection ◽

Quadratic Program ◽

Modularity Maximization

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A spectral clustering approach to underdetermined postnonlinear blind source separation of sparse sources

IEEE Transactions on Neural Networks ◽

10.1109/tnn.2006.872358 ◽

2006 ◽

Vol 17 (3) ◽

pp. 811-814 ◽

Cited By ~ 17

Author(s):

S. Van Vaerenbergh ◽

I. Santamaria

Keyword(s):

Blind Source Separation ◽

Spectral Clustering ◽

Source Separation ◽

Clustering Approach

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Incremental Community Detection on Large Complex Attributed Network

ACM Transactions on Knowledge Discovery from Data ◽

10.1145/3451216 ◽

2021 ◽

Vol 15 (6) ◽

pp. 1-20

Author(s):

Zhe Chen ◽

Aixin Sun ◽

Xiaokui Xiao

Keyword(s):

Community Detection ◽

Large Scale ◽

Network Data ◽

Topological Information ◽

Community Membership ◽

Attributed Network ◽

Benchmark Datasets ◽

Modularity Maximization ◽

Large Scale Networks

Community detection on network data is a fundamental task, and has many applications in industry. Network data in industry can be very large, with incomplete and complex attributes, and more importantly, growing. This calls for a community detection technique that is able to handle both attribute and topological information on large scale networks, and also is incremental. In this article, we propose inc-AGGMMR, an incremental community detection framework that is able to effectively address the challenges that come from scalability, mixed attributes, incomplete values, and evolving of the network. Through construction of augmented graph, we map attributes into the network by introducing attribute centers and belongingness edges. The communities are then detected by modularity maximization. During this process, we adjust the weights of belongingness edges to balance the contribution between attribute and topological information to the detection of communities. The weight adjustment mechanism enables incremental updates of community membership of all vertices. We evaluate inc-AGGMMR on five benchmark datasets against eight strong baselines. We also provide a case study to incrementally detect communities on a PayPal payment network which contains users with transactions. The results demonstrate inc-AGGMMR’s effectiveness and practicability.

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