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Community detection for emerging social networks

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Abstract

Many famous online social networks, e.g., Facebook and Twitter, have achieved great success in the last several years. Users in these online social networks can establish various connections via both social links and shared attribute information. Discovering groups of users who are strongly connected internally is defined as the community detection problem. Community detection problem is very important for online social networks and has extensive applications in various social services. Meanwhile, besides these popular social networks, a large number of new social networks offering specific services also spring up in recent years. Community detection can be even more important for new networks as high quality community detection results enable new networks to provide better services, which can help attract more users effectively. In this paper, we will study the community detection problem for new networks, which is formally defined as the “New Network Community Detection” problem. New network community detection problem is very challenging to solve for the reason that information in new networks can be too sparse to calculate effective similarity scores among users, which is crucial in community detection. However, we notice that, nowadays, users usually join multiple social networks simultaneously and those who are involved in a new network may have been using other well-developed social networks for a long time. With full considerations of network difference issues, we propose to propagate useful information from other well-established networks to the new network with efficient information propagation models to overcome the shortage of information problem. An effective and efficient method, Cat (Cold stArT community detector), is proposed in this paper to detect communities for new networks using information from multiple heterogeneous social networks simultaneously. Extensive experiments conducted on real-world heterogeneous online social networks demonstrate that Cat can address the new network community detection problem effectively.

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Acknowledgments

This work is supported in part by NSF through grants IIS-1526499, and CNS-1626432, and NSFC 61672313. It is also supported by the National Key R&D Program of China (Grant No. 2016YFB1001102) and NSFC (Grant No.61375069, 61403156, 61502227) and the Collaborative Innovation Center of Novel Software Technology and Industrialization, Nanjing University.

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Authors and Affiliations

  1. National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China

    Qianyi Zhan & Junyuan Xie

  2. University of Illinois at Chicago, Chicago, IL, 60607, USA

    Jiawei Zhang & Philip Yu

  3. Institute for Data Science, Tsinghua University, Beijing, China

    Philip Yu

Authors
  1. Qianyi Zhan
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  2. Jiawei Zhang
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  3. Philip Yu
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  4. Junyuan Xie
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Corresponding author

Correspondence to Qianyi Zhan.

Appendix

Appendix

1.1 A Proof of Lemma 2

Proof

The Lemma can be proved by induction on k [26] as follows:Base Case: When k = 1, let p i and λ i be the i th eigenvector and eigenvalue of matrix Q respectively, where Qp i = λ i p i . Organizing all the eigenvectors and eigenvalues of Q in matrix P and Λ, we can have Q 1 P = PΛ1.

Inductive Assumption: When k = m, m ≥ 1, let’s assume the lemma holds when k = m, m ≥ 1. In other words, the following equation holds:

$$\mathbf{Q}^m\mathbf{P} = \mathbf{P}\mathbf{\Lambda}^m. $$

Induction: When k = m+1, m ≥ 1,

$$\mathbf{Q}^{(m + 1)}\mathbf{P} = \mathbf{Q}\mathbf{Q}^m\mathbf{P}= \mathbf{Q}\mathbf{P}\mathbf{\Lambda}^m\\ =\mathbf{P}\mathbf{\Lambda}\mathbf{\Lambda}^m =\mathbf{P}\mathbf{\Lambda}^{(m + 1)}. $$

In sum, the lemma holds for k ≥ 1. □

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Zhan, Q., Zhang, J., Yu, P. et al. Community detection for emerging social networks. World Wide Web 20, 1409–1441 (2017). https://doi.org/10.1007/s11280-017-0441-5

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