Although previous graph-based multi-view clustering (MVC) algorithms have gained significant progress, most of them are still faced with three limitations. First, they often suffer from high computational complexity, which restricts their applications in large-scale scenarios. Second, they usually perform graph learning either at the single-view level or at the view–consensus level, but often neglect the possibility of the joint learning of single-view and consensus graphs. Third, many of them rely on the $k$ -means for discretization of the spectral embeddings, which lack the ability to directly learn the graph with discrete cluster structure. In light of this, this article presents an efficient MVC approach via u nified and d iscrete b ipartite g raph l earning (UDBGL). Specifically, the anchor-based subspace learning is incorporated to learn the view-specific bipartite graphs from multiple views, upon which the bipartite graph fusion is leveraged to learn a view–consensus bipartite graph with adaptive weight learning. Furthermore, the Laplacian rank constraint is imposed to ensure that the fused bipartite graph has discrete cluster structures (with a specific number of connected components). By simultaneously formulating the view-specific bipartite graph learning, the view–consensus bipartite graph learning, and the discrete cluster structure learning into a unified objective function, an efficient minimization algorithm is then designed to tackle this optimization problem and directly achieve a discrete clustering solution without requiring additional partitioning, which notably has linear time complexity in data size. Experiments on a variety of multi-view datasets demonstrate the robustness and efficiency of our UDBGL approach. The code is available at https://github.com/huangdonghere/UDBGL.

Community detection is one of the popular research topics in the field of complex networks analysis. It aims to identify communities, represented as cohesive subgroups or clusters, where nodes in the same community link to each other more densely than others outside. Due to the interpretability, simplicity, flexibility, and generality, nonnegative matrix factorization (NMF) has become a very ideal model for community detection and lots of related methods have been presented. To facilitate research on NMF-based community detection, in this article, we make a comprehensive review on NMF-based methods for community detection, especially the state-of-the-art methods presented in high prestige journals or conferences. First, we introduce the basic principles of NMF and explain why NMF can detect communities and design a general framework of NMF-based community detection. Second, according to the applicable network types, we propose a taxonomy to divide the existing NMF-based methods for community detection into six categories, namely, topology networks, signed networks, attributed networks, multilayer networks, dynamic networks, and large-scale networks. We deeply analyze representative methods in every category. Finally, we summarize the common problems faced by all methods and potential solutions and propose four promising research directions. We believe that this survey can fully demonstrate the versatility of NMF-based community detection and serve as a useful guideline for researchers in related fields.

Community detection is of great help to understand the structures and functions of complex networks. It has become one of popular research topics in the field of complex networks analysis. Due to the simplicity, flexibility, effectiveness and better interpretability, Nonnegative Matrix Factorization (NMF)-based methods have been widely employed for community detection. However, most existing NMF-based community detection methods are linear and their performance is limited when facing networks with diversified structure information. In view of this, we propose a nonlinear NMF-based method named NMFGAAE, which is composed of two main modules: NMF and Graph Attention Auto-Encoder (GAAE). This approach can boost the performance of NMF-based community detection methods by the aid of graph neural networks and deep clustering. More specifically, GAAE introduces an attention mechanism directed by NMF-based community detection to learn the node representations, while NMF can simultaneously factor these representations to uncover the community structure. We design a unified framework to jointly optimize GAAE and NMF modules, which is very beneficial to obtain better community detection results. We conduct extensive experiments on synthetic and real-world networks. The results show that our NMFGAAE not only performs better than state-of-the-art NMF-based community detection methods, but also outperforms some network representation based baselines. More importantly, NMFGAAE indeed can boost the performance of NMF-based community detection methods.

Currently, community detection in signed networks has become a popular research topic due to the widespread use of signed networks for modeling relationships among entities in the real world. However, most of these existing graph neural network-based methods still have two limitations. The first one is that these methods are not applicable for the directed and weighted signed networks, and the second one is that the GNN methods cannot consider the network community structure, resulting in the learned node features failing to capture community-oriented characteristics. In view of these limitations, this paper proposes a directed weighted signed graph convolutional network for community detection called DWSGCN. For the first limitation, we introduce novel aggregation strategies based on two social psychological theories and construct a weighted adjacency matrix to fully extract the direction and weight information of links. In order to obtain the community-oriented node embedding, a novel modularity maximization loss is designed for signed networks and combined with a structure loss to jointly optimize DWSGCN. Finally, we obtain the community results in an end-to-end manner. Extensive experiments demonstrate the superiority of DWSGCN over most state-of-the-art approaches.