Journal
IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING
Volume 31, Issue 2, Pages 273-286Publisher
IEEE COMPUTER SOC
DOI: 10.1109/TKDE.2018.2832205
Keywords
Multi-layer networks; community structure; nonnegative matrix factorization; semi-supervised clustering
Categories
Funding
- NSFC [61772394, 61502363, 61572385]
- International Cooperation and Exchange of the NSFC [61711530248]
- Science AMP
- Technology Program of Shannxi Province [2015KTCXSF-01]
- Fundamental Research Funding of Central Universities [JB180304]
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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 K-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 Semi-Supervised joint Nonnegative Matrix Factorization algorithm (S2-jNMF) 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.
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