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Optimization of identifiability for efficient community detection

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jats:titleAbstract</jats:title> jats:pMany physical and social systems are best described by networks. And the structural properties of these networks often critically determine the properties and function of the resulting mathematical models. An important method to infer the correlations between topology and function is the detection of community structure, which plays a key role in the analysis, design, and optimization of many complex systems. The nonnegative matrix factorization has been used prolifically to that effect in recent years, although it cannot guarantee balanced partitions, and it also does not allow a proactive computation of the number of communities in a network. This indicates that the nonnegative matrix factorization does not satisfy all the nonnegative low-rank approximation conditions. Here we show how to resolve this important open problem by optimizing the identifiability of community structure. We propose a new form of nonnegative matrix decomposition and a probabilistic surrogate learning function that can be solved according to the majorization–minimization principle. Extensive jats:italicin silico</jats:italic> tests on artificial and real-world data demonstrate the efficient performance in community detection, regardless of the size and complexity of the network.</jats:p>



complex system, complex network, community detection, matrix factorization

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New Journal of Physics

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IOP Publishing
National Natural Science Foundation of China (11975025 71573051 71871109 71871233 71873039)
Natural Science Foundation of Beijing Municipality (9182015)
Javna Agencija za Raziskovalno Dejavnost RS (J1-9112 J4-9302 P1-0403)