Principled Multilayer Network Embedding

Multilayer network analysis has become a vital tool for understanding different relationships and their interactions in a complex system, where each layer in a multilayer network depicts the topological structure of a group of nodes corresponding to a particular relationship. The interactions among different layers imply how the interplay of different relations on the topology of each layer. For a single-layer network, network embedding methods have been proposed to project the nodes in a network into a continuous vector space with a relatively small number of dimensions, where the space embeds the social representations among nodes. These algorithms have been proved to have a better performance on a variety of regular graph analysis tasks, such as link prediction, or multi-label classification. In this paper, by extending a standard graph mining into multilayer network, we have proposed three methods ("network aggregation," "results aggregation" and "layer co-analysis") to project a multilayer network into a continuous vector space. On one hand, without leveraging interactions among layers, "network aggregation" and "results aggregation" apply the standard network embedding method on the merged graph or each layer to find a vector space for multilayer network. On the other hand, in order to consider the influence of interactions among layers, "layer co-analysis" expands any single-layer network embedding method to a multilayer network. By introducing the link transition probability based on information distance, this method not only uses the first and second order random walk to traverse on a layer, but also has the ability to traverse between layers by leveraging interactions. From the evaluation, we have proved that comparing with regular link prediction methods, "layer co-analysis" achieved the best performance on most of the datasets, while "network aggregation" and "results aggregation" also have better performance than regular link prediction methods.