Community Detection in Multi-Layer Networks Using Joint Nonnegative Matrix Factorization

Many complex systems are composed of coupled networks through different layers, where each layer represents one of many possible types of interactions. A fundamental question is how to extract communities in multi-layer networks. The current algorithms either collapses multi-layer networks into a single-layer network or extends the algorithms for single-layer networks by using consensus clustering. However, these approaches have been criticized for ignoring the connection among various layers, thereby resulting in low accuracy. To attack this problem, a quantitative function (multi-layer modularity density) is proposed for community detection in multi-layer networks. Afterward, we prove that the trace optimization of multi-layer modularity density is equivalent to the objective functions of algorithms, such as kernel <inline-formula><tex-math notation="LaTeX">$K$</tex-math><alternatives><inline-graphic xlink:href="ma-ieq1-2832205.gif"/></alternatives></inline-formula>-means, nonnegative matrix factorization (NMF), spectral clustering and multi-view clustering, for multi-layer networks, which serves as the theoretical foundation for designing algorithms for community detection. Furthermore, a <underline>S</underline>emi-<underline>S</underline>upervised <underline>j</underline>oint <underline>N</underline>onnegative <underline>M</underline>atrix <underline>F</underline>actorization algorithm (<italic>S2-jNMF</italic>) is developed by simultaneously factorizing matrices that are associated with multi-layer networks. Unlike the traditional semi-supervised algorithms, the partial supervision is integrated into the objective of the S2-jNMF algorithm. Finally, through extensive experiments on both artificial and real world networks, we demonstrate that the proposed method outperforms the state-of-the-art approaches for community detection in multi-layer networks.

• Publication year

  2019

• Venue

  IEEE Transactions on Knowledge and Data Engineering

• Publication date

  2019-02-01

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1109/TKDE.2018.2832205
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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