Exploratory Data Analysis for Multiplex Networks with DISTATIS

Multilayer network data arises when there exists more than one source of relationship for a group of actors (Kivelä et al., 2014, and references therein). For such kind of data, the usual approach consists in dealing with multiple relations separately or in summing up the information embedded in all layers. This latter reduces the complexity of multiplex data and may lead to a loss of relevant information. In the present contribution, aiming at visually explore the complex structure of multilayer networks, we propose to use factorial methods. These methods, in fact, have proven to be suitable to analyze the set of multiple relations seen as a whole complex structure (D’Esposito et al., 2014, Ragozini et al., 2015, Zhu et al. 2016). More specifically, given the data structure of one-mode multilayer networks, we propose to analyze the corresponding set of the adjacency matrices through the DISTATIS technique (Abdi et al., 2012), which is an extension of the multidimensional scaling to a set of connected distance matrices. This technique, in a STATIS perspective (Lavit et al., 1984), allows to represent the different kinds of relationships (inter-structures) in separa te spaces and in a compromise space. By the use of DISTATIS we will be able to visually explore: i) the network structure in terms of actor similarity in each single layer, ii) the common structure of all layers, iii) the actor variations across layers, and iv) the similarities among layer structures. The proposed method will be discussed within some illustrative examples.