Clustering of Multilayer Networks Using Joint Learning Algorithm With Orthogonality and Specificity of Features

Complex systems in nature and society consist of various types of interactions, where each type of interaction belongs to a layer, resulting in the so-called multilayer networks. Identifying specific modules for each layer is of great significance for revealing the structure-function relations in multilayer networks. However, the available approaches are criticized undesirable because they fail to explicitly the specificity of modules, and balance the specificity and connectivity of modules. To overcome these drawbacks, we propose an accurate and flexible algorithm by joint learning matrix factorization and sparse representation (jMFSR) for specific modules in multilayer networks, where matrix factorization extracts features of vertices and sparse representation discovers specific modules. To exploit the discriminative latent features of vertices in multilayer networks, jMFSR incorporates linear discriminant analysis (LDA) into non-negative matrix factorization (NMF) to learn features of vertices that distinguish the categories. To explicitly measure the specificity of features, jMFSR decomposes features of vertices into common and specific parts, thereby enhancing the quality of features. Then, jMFSR jointly learns feature extraction, common-specific feature factorization, and clustering of multilayer networks. The experiments on 11 datasets indicate that jMFSR significantly outperforms state-of-the-art baselines in terms of various measurements.