Wu Wenming, Gong Maoguo, Ma Xiaoke
IEEE Trans Cybern. 2023 Aug;53(8):4972-4985. doi: 10.1109/TCYB.2022.3152723. Epub 2023 Jul 18.
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.
自然界和社会中的复杂系统由各种类型的相互作用组成，其中每种相互作用都属于一个层次，从而形成了所谓的多层网络。识别每层的特定模块对于揭示多层网络中的结构-功能关系具有重要意义。然而，现有的方法受到批评，因为它们没有明确模块的特异性，也没有平衡模块的特异性和连通性。为了克服这些缺点，我们提出了一种精确且灵活的算法——联合学习矩阵分解与稀疏表示（jMFSR），用于多层网络中的特定模块，其中矩阵分解提取顶点特征，稀疏表示发现特定模块。为了利用多层网络中顶点的判别性潜在特征，jMFSR将线性判别分析（LDA）纳入非负矩阵分解（NMF）以学习区分类别的顶点特征。为了明确测量特征的特异性，jMFSR将顶点特征分解为公共部分和特定部分，从而提高特征质量。然后，jMFSR联合学习多层网络的特征提取、公共-特定特征分解和聚类。在11个数据集上的实验表明，jMFSR在各种测量指标上显著优于当前最先进的基线方法。
