Embedding regularized nonnegative matrix factorization for structural reduction in multi-layer networks

Abstract A variety of complex systems from nature and society, ranging from biological to technological systems, can be effectively modeled by networks. The multiplex character of real-world systems leads to distinct types of interactions that are categorized as edges belonging to various layers. And, the topological analysis of multi-layer networks discovers graph patterns that are critical for revealing the mechanisms of systems. An essential prerequisite of successful multi-layer networks analysis is how to remove the redundancy of networks, i.e., structural reduction of multi-layer networks. The current algorithms quantify the distance among various layers by using either the topological structure or the representative vectors, which fail to fully characterize the relationship among various layers, leading to low accuracy. To overcome this problem, we propose a nonnegative matrix factorization algorithm for multi-layer networks reduction (NMF-MNR), which jointly factorizes the topological structure and graph representation of various layers. Specifically, we adopt the network embedding to obtain low-dimensional graph representation of each layer, and then jointly decompose the adjacency matrix and graph representation to extract the feature matrix for each layer, which provides a better way to characterize layers of networks. The experimental results on both artificial and real-world networks demonstrate that NMF-MNR is more accurate and robust than state-of-the-art approaches.