Community detection in multiplex networks using orthogonal non-negative matrix tri-factorization based on graph regularization and diversity

In recent years, community detection has received increasing interest. In network analysis, community detection refers to the identification of tightly connected subsets of nodes, which are called “communities” or “groups”, in the network. Non-negative matrix factorization models are often used to solve the problem. Orthogonal non-negative matrix tri-factorization (ONMTF) exhibits significant potential as an approach for community detection within multiplex networks. This paper explores the application of ONMTF in multiplex networks, aiming to detect both shared and exclusive communities simultaneously. The model decomposes each layer within the multiplex network into two low-rank matrices. One matrix corresponds to shared communities across all layers, and the other to unique communities within each layer. Additionally, graph regularization and the diversity of private communities are taken into account in the algorithm. The Hilbert Schmidt Independence Criterion (HSIC) is used to constrain the independence of private communities. The results prove that ONMTF effectively addresses community detection in multiplex networks. It also offers strong interpretability and feature extraction capabilities. Therefore, it is an advanced method for community detection in multiplex networks.</p

Robust multi-view non-negative matrix factorization with adaptive graph and diversity constraints

Multi-view clustering (MVC) has received extensive attention due to its efficient processing of high-dimensional data. Most of the existing multi-view clustering methods are based on non-negative matrix factorization (NMF), which can achieve dimensionality reduction and interpretable representation. However, there are following issues in the existing researches: (1) The existing methods based on NMF using Frobenius norm are sensitive to noises and outliers. (2) Many methods only use the information shared by multi-view data, while ignoring the diverse information between views. (3) The data graph constructed by the conventional K Nearest Neighbors (KNN) method may misclassify neighbors and degrade the clustering performance. To address the above problems, we propose a novel robust multi-view clustering method. Specifically, -norm is introduced to measure the factorization error to improve the robustness of NMF. Additionally, a diversity constraint is utilized to learn the diverse relationship of multi-view data, and an adaptive graph method via information entropy is designed to overcome the shortcomings of misclassifying neighbors. Finally, an iterative updating algorithm is developed to solve the optimization model, which can make the objective function monotonically non-increasing. The effectiveness of the proposed method is substantiated by comparing with eleven state-of-the-art methods on five real-world and four synthetic multi-view datasets for clustering tasks