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. 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

Feature-rich networks: going beyond complex network topologies.

Abstract The growing availability of multirelational data gives rise to an opportunity for novel characterization of complex real-world relations, supporting the proliferation of diverse network models such as Attributed Graphs, Heterogeneous Networks, Multilayer Networks, Temporal Networks, Location-aware Networks, Knowledge Networks, Probabilistic Networks, and many other task-driven and data-driven models. In this paper, we propose an overview of these models and their main applications, described under the common denomination of Feature-rich Networks, i. e. models where the expressive power of the network topology is enhanced by exposing one or more peculiar features. The aim is also to sketch a scenario that can inspire the design of novel feature-rich network models, which in turn can support innovative methods able to exploit the full potential of mining complex network structures in domain-specific applications

Stochastic block-models for multiplex networks:An application to a multilevel network of researchers

Modelling relationships between individuals is a classical question in social sci- ences and clustering individuals according to the observed patterns of interactions allows us to uncover a latent structure in the data. The stochastic block model is a popular approach for grouping individuals with respect to their social comportment. When several relationships of various types can occur jointly between individuals, the data are represented by multiplex networks where more than one edge can exist between the nodes. We extend stochastic block models to multiplex networks to obtain a clustering based on more than one kind of relation- ship. We propose to estimate the parameters—such as the marginal probabilities of assignment to groups (blocks) and the matrix of probabilities of connections between groups—through a variational expectation–maximization procedure. Consistency of the estimates is studied. The number of groups is chosen by using the integrated completed likelihood criterion, which is a penalized likelihood criterion. Multiplex stochastic block models arise in many situations but our applied example is motivated by a network of French cancer researchers. The two possi- ble links (edges) between researchers are a direct connection or a connection through their laboratories. Our results show strong interactions between these two kinds of connection and the groups that are obtained are discussed to emphasize the common features of researchers grouped together