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DEEPLEX: A GNN FOR LINK PREDICTION IN MULTIPLEX NETWORKS

Graph neural networks have recently gained attention due to their performance in many classification and prediction tasks. In particular, they are used for node classification and link prediction which has a wide range of applications in social networks, biomedical datasets and financial transaction graphs. Most of the existing work is primarly focused on the monoplex setting where we have access to a network with only a single type of connections between entities. However, in the multiplex setting, where there are multiple types of connections between entities, tasks such as link prediction have been shown to have stronger performance when information from other connection types is taken into account. We notice a critical issue with a previous approach, MNE, based on embedding models related to the way information is aggregated across layers and propose a novel method DeePlex which aggregates layer information using a neural network. Experimental results on real-world multiplex networks show that our approach outperforms and overcomes the limitations of state of the art approaches. Introduction One of the fundamental problems in network analysis is that of link prediction. Quite a few approaches have been proposed to solve this problem and they can be broadly classified into two categories: (A) Supervised methods (B) Heuristic methods [5]. Heuristic approaches while relatively simple and easy to compute in most cases are surprisingly good in performance over a wide-range of network domains. Examples in this class are common neighbors (CN), Adamic-Adar [1], and Katz. In many real-world settings two nodes may be connected over multiple facets. For example, consider the trading patterns across the countries of the world where two countries are connected if they trade a particular commodity like say rice. If we then consider all the commodities then we see a rich pattern of connectivity between the nodes and this notion is called multiplexity or a multiplex network. A straightforward approach would be to treat each layer of the separately and apply either the supervised or heuristic methods. However, this may not be ideal because we are not utilizing the rich structure of correlations across the various layers that may exist in the network. We propose to use the graph neural network (GNN) framework to embed the sub-graphs corresponding to the various layers of the networks and jointly learn classifier which weighs these embeddings to predict the existence of links in the corresponding layer. To the best of our knowledge, this is the first work which combines GNN for multiplex link prediction problem. Additionally, we utilize label information from the other layers. SEAL We use an existing approach for obtaining node embeddings for a given network namely SEAL [7]. It learns the node structural features based on the local enclosing subgraphs. SEAL is flexible in which GNN architecture that it uses and we retain DGCNN [8] as our default. Experimental results show them to be significantly better than other link prediction algorithms such as node2vec (N2V) [2], spectral clustering (SPC) and variational graph auto-encoder (VGAE) [4]. MNE A popular approach for link prediction in multiplex networks is the recently proposed embedding approach MNE [6]. The idea is to learn a common “base” embedding utilizing all the links in all the networks and individual node embeddings for each of the layers and combining these two to obtain the final node embedding. In particular for each node, they propose to learn a highdimensional common embedding across all the layers and a smaller embedding for each individual layer. The two embeddings are combined via a linear transformation which is learnt from the training data. Concretely, given a network of layers G1, ·, GL where we have L layers and Gi = (Ni, Ei) corresponding to sets of Ni nodes and Ei edges, MNE learns a node embedding: v n = bn+w Ẋ T un where X ∈ Rs×d, bn correspond to the base node embedding and un to the individual node embedding for the layer. DeePlex We set out to take the best elements of both the approaches while potentially avoiding the limitations of