Structural property-aware multilayer network embedding for latent factor analysis

Multilayer network is a structure commonly used to describe and model the complex interaction between sets of entities/nodes. A three-layer example is the author-paper-word structure in which authors are linked by co-author relation, papers are linked by citation relation, and words are linked by semantic relation. Network embedding, which aims to project the nodes in the network into a relatively low-dimensional space for latent factor analysis, has recently emerged as an effective method for a variety of network-based tasks, such as collaborative filtering and link prediction. However, existing studies of network embedding both focus on the single-layer network and overlook the structural properties of the network, e.g., the degree distribution and communities, which are significant for node characterization, such as the preferences of users in a social network. In this paper, we propose four multilayer network embedding algorithms based on Nonnegative Matrix Factorization (NMF) with consideration given to four structural properties: whole network (NNMF), community (CNMF), degree distribution (DNMF), and max spanning tree (TNMF). Experiments on synthetic data show that the proposed algorithms are able to preserve the desired structural properties as designed. Experiments on real-world data show that multilayer network embedding improves the accuracy of document clustering and recommendation, and the four embedding algorithms corresponding to the four structural properties demonstrate the differences in performance on these two tasks. These results can be directly used in document clustering and recommendation systems.