Overlapping community detection via Layer-Jaccard similarity incorporated nonnegative matrix factorization.

As information modernization progresses, the connections between entities become more elaborate, forming more intricate networks. Consequently, the emphasis on community detection has transitioned from discerning disjoint communities towards the identification of overlapping communities. A variety of algorithms based on the sparse adjacency matrix, which are sensitive to edge connections, are suitable for detecting edge-sparse areas between overlapping communities but lack the ability to detect edge-dense areas within the overlapping communities. Additionally, most algorithms do not take into account multihop information. To mitigate the aforementioned limitations, we propose an innovative approach termed Layer-Jaccard similarity incorporated nonnegative matrix factorization (LJSINMF), which utilizes both the adjacency matrix and the Layer-Jaccard similarity matrix. Our method initially employs a newly proposed Onion-shell method to decompose the network into layers. Subsequently, the layer of each node is used to construct a Layer-Jaccard similarity matrix, which facilitates the identification of edge-dense areas within the overlapping communities and serves as a general approach for enhancing other nonnegative matrix factorization-based algorithms. Ultimately, we integrate the adjacency matrix and the Layer-Jaccard similarity matrix into the nonnegative matrix factorization framework to determine the node-community membership matrix. Moreover, integrating the Layer-Jaccard similarity matrix into other algorithms is a promising approach to enhance their performance. Comprehensive experiments have been conducted on real-world networks and the results substantiate that the LJSINMF algorithm outperforms most state-of-the-art baseline methods in terms of three evaluation metrics.