Multiplex Embedding of Biological Networks Using Cross-Network Node Similarities

Network embedding techniques, which provide low-dimensional representations of the nodes in a network, have been commonly applied to many machine learning problems in computational biology. In most of these applications, multiple networks (e.g., different types of interactions/associations or semantically identical networks that come from different sources) are available. Multiplex network embedding aims to derive strength from these data sources by integrating multiple networks that share a common set of nodes. Existing approaches to this problem treat all layers of the multiplex network separately while performing integration, ignoring the differences in the topology and sparsity patterns of different networks. Here, we formulate an optimization problem that accounts for inner-network smoothness and topological similarity of networks to compute diffusion states for each network. To quantify the topological similarity of nodes in different networks, we utilize shared neighborhood across networks. To compute the diffusion states of integrated networks, we propose an efficient algorithm for accelerating iterations, which yields two-fold improvement over the runtime of the state-of-the-art power iteration techniques. Finally, we integrate the resulting diffusion states and apply dimensionality reduction (singular value decomposition after log transformation) to compute node embeddings. We evaluate the performance of the resulting algorithm, Crossim, in the context of protein function prediction. Our experimental results show that the embeddings computed by Crossim consistently improve predictive accuracy over algorithms that do not take into account the topological similarity of different networks, suggesting that accounting for topological similarity across multiple network layers can improve network integration.