Community Detection in Signed Networks Based on Normalized Laplacian Matrix and Convex Non-negative Matrix Factorization

Signed networks can intuitively and flexibly describe the positive and negative interactions among entities in a complex network. Community structure detection is a basic research topic of signed network analysis, which is of theoretical significance and practical value to reveal the organizational structure, functional structure, and individual behavior of complex systems. However, it is still a challenging task to accurately detect the community structure in a signed network. In this paper, we design a community detection algorithm based on normalized Laplacian matrix and convex non-negative matrix factorization for signed networks. The proposed algorithm applies convex non-negative matrix decomposition to a signed network, and decomposes the adjacency matrix of the network into a community membership matrix and a node weight matrix. Meanwhile, the algorithm introduces normalized Laplacian graph regularization terms to reduce noise generated during the decomposition process. Experimental results verify that the proposed algorithm is effective in community detection.