Analyzing multiplex networks using factorial methods

Abstract Multiplex networks arise when more than one source of relationships exists for a common set of nodes. Many approaches to deal with this kind of complex network data structure are reported in the literature. In this paper, we propose the use of factorial methods to visually explore the complex structure of multiplex networks. Specifically, the adjacency matrices derived from multiplex networks are analyzed using the DISTATIS technique, an extension of multidimensional scaling to three-way data. This technique allows the representation of the different types of relationships in both separate spaces for each layer and a compromise space. The analytical procedure is illustrated using a real world example and simulated data.

[1]  Rushed Kanawati,et al.  Community detection in multiplex networks: A seed-centric approach , 2015, Networks Heterog. Media.

[2]  Jorge Cadima,et al.  Principal component analysis: a review and recent developments , 2016, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[3]  Valentina Kuskova,et al.  Correspondence Analysis of Multirelational Multilevel Networks , 2016 .

[4]  Raine Hoover,et al.  Investor commitment to serial entrepreneurs: A multilayer network analysis , 2017, Soc. Networks.

[5]  Termeh Shafie,et al.  A Multigraph Approach to Social Network Analysis , 2015, J. Soc. Struct..

[6]  Matteo Magnani,et al.  Introduction to the special issue on multilayer networks , 2017, Network Science.

[7]  Emmanuel Lazega,et al.  Multiplexity, generalized exchange and cooperation in organizations: a case study , 1999, Soc. Networks.

[8]  Michael T. Heaney,et al.  Multiplex networks and interest group influence reputation: An exponential random graph model , 2014, Soc. Networks.

[9]  Paola Zappa,et al.  Dynamic patterns analysis meets Social Network Analysis in the modeling of financial market behavior , 2013 .

[10]  S. Wasserman,et al.  Logit models and logistic regressions for social networks: II. Multivariate relations. , 1999, The British journal of mathematical and statistical psychology.

[11]  Giancarlo Ragozini,et al.  On the Analysis of Time-Varying Affiliation Networks: The Case of Stage Co-productions , 2016 .

[12]  Matteo Magnani,et al.  Multilayer Social Networks , 2016 .

[13]  Peng Wang,et al.  Exponential Random Graph Models for Social Networks: Exponential Random Graph Model Extensions: Models for Multiple Networks and Bipartite Networks , 2012 .

[14]  Termeh Shafie,et al.  Analyzing local and global properties of multigraphs , 2016 .

[15]  Robert L. Mason,et al.  Fractional factorial design , 2009 .

[16]  Vito Latora,et al.  Structural reducibility of multilayer networks , 2015, Nature Communications.

[17]  Giovanni Montana,et al.  Community detection in multiplex networks using Locally Adaptive Random walks , 2015, 2015 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM).

[18]  Giancarlo Ragozini,et al.  Multiple factor analysis for time-varying two-mode networks , 2015, Network Science.

[19]  V. Batagelj,et al.  Comparing resemblance measures , 1995 .

[20]  Joseph L. Zinnes,et al.  Theory and Methods of Scaling. , 1958 .

[21]  András Vörös,et al.  Cluster analysis of multiplex networks: Defining composite network measures , 2017, Soc. Networks.

[22]  Hervé Abdi,et al.  STATIS and DISTATIS: optimum multitable principal component analysis and three way metric multidimensional scaling , 2012 .

[23]  Barbora Micenková,et al.  Clustering attributed graphs: Models, measures and methods , 2015, Network Science.

[24]  Giancarlo Ragozini,et al.  On the use of Multiple Correspondence Analysis to visually explore affiliation networks , 2014, Soc. Networks.

[25]  Ulrike Groemping,et al.  CRAN Task View: Design of Experiments (DoE) & Analysis of Experimental Data , 2020 .

[26]  Giancarlo Ragozini,et al.  A Comparison of χ 2 Metrics for the Assessment of Relational Similarities in Affiliation Networks , 2014 .

[27]  Philip S. Yu,et al.  Multi-task Network Embedding , 2017, 2017 IEEE International Conference on Data Science and Advanced Analytics (DSAA).

[28]  Hervé Abdi,et al.  How to compute reliability estimates and display confidence and tolerance intervals for pattern classifiers using the Bootstrap and 3-way multidimensional scaling (DISTATIS) , 2009, NeuroImage.

[29]  Sergio Gómez,et al.  Centrality rankings in multiplex networks , 2014, WebSci '14.

[30]  J. Gower,et al.  Metric and Euclidean properties of dissimilarity coefficients , 1986 .

[31]  I. Mechelen,et al.  Three-way component analysis: principles and illustrative application. , 2001, Psychological methods.

[32]  Cohen R. Simpson.  Multiplexity and strategic alliances: The relational embeddedness of coalitions in social movement organisational fields , 2015, Soc. Networks.

[33]  Miguel Romance,et al.  Eigenvector centrality of nodes in multiplex networks , 2013, Chaos.

[34]  Ginestra Bianconi,et al.  Weighted Multiplex Networks , 2013, PloS one.

[35]  Giancarlo Ragozini,et al.  Quantifying layer similarity in multiplex networks: a systematic study , 2017, Royal Society Open Science.

[36]  Rushed Kanawati,et al.  Multiplex Network Mining: A Brief Survey , 2015, IEEE Intell. Informatics Bull..

[37]  Alice J. O'Toole,et al.  DISTATIS: The Analysis of Multiple Distance Matrices , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Workshops.

[38]  Dominique Valentin,et al.  Analyzing assessors and products in sorting tasks: DISTATIS, theory and applications , 2007 .

[39]  Tsuyoshi Murata,et al.  MELL: Effective Embedding Method for Multiplex Networks , 2018, WWW.

[40]  Maria Prosperina Vitale,et al.  FACTORIAL CONTIGUITY MAPS TO EXPLORE RELATIONAL DATA PATTERNS 1 , 2007 .

[41]  J. Antonio Rivero Ostoic,et al.  Creating context for social influence processes in multiplex networks , 2017, Network Science.

[42]  Patrick Doreian,et al.  Multiobjective Blockmodeling for Social Network Analysis , 2012, Psychometrika.

[43]  Hildegarde Heymann,et al.  Rapid sensory profiles with DISTATIS and Barycentric Text Projection: An example with amari , bitter herbal liqueurs , 2018, Food Quality and Preference.

[44]  John Scott,et al.  Using Correspondence Analysis for Joint Displays of Affiliation Networks , 2005 .

[45]  S. Boorman,et al.  Social Structure from Multiple Networks. I. Blockmodels of Roles and Positions , 1976, American Journal of Sociology.

[46]  Giuseppe Giordano,et al.  On the use of external information in social network analysis , 2011, Adv. Data Anal. Classif..

[47]  Dominique Valentin,et al.  SOME NEW AND EASY WAYS TO DESCRIBE, COMPARE, AND EVALUATE PRODUCTS AND ASSESSORS , 2007 .

[48]  Ginestra Bianconi,et al.  Multiplex PageRank , 2013, PloS one.

[49]  Matteo Magnani,et al.  A Generalized Force-Directed Layout for Multiplex Sociograms , 2018, SocInfo.

[50]  Linton C. Freeman,et al.  Models and Methods in Social Network Analysis: Graphic Techniques for Exploring Social Network Data , 2001 .

[51]  Susanna Zaccarin,et al.  Modelling Multiple Interactions in Science and Technology Networks , 2013 .

[52]  Charles Carroll,et al.  Canonical correlation analysis: Assessing links between multiplex networks , 2006, Soc. Networks.

[53]  Y. Escoufier.  Objectifs et procédures de l'analyse conjointe de plusieurs tableaux de données , 1985 .

[54]  Alessandro Lomi,et al.  A model for the multiplex dynamics of two-mode and one-mode networks, with an application to employment preference, friendship, and advice , 2013, Soc. Networks.

[55]  E. Lazega,et al.  Stochastic block models for multiplex networks: an application to a multilevel network of researchers , 2017 .

[56]  Mason A. Porter,et al.  Multilayer networks , 2013, J. Complex Networks.

[57]  John M. Roberts.  Correspondence analysis of two-mode network data , 2000, Soc. Networks.

[58]  Dominique Valentin,et al.  Free sorting task , 2014 .

[59]  Jukka-Pekka Onnela,et al.  Community Structure in Time-Dependent, Multiscale, and Multiplex Networks , 2009, Science.

[60]  Ginestra Bianconi,et al.  Multilayer Networks , 2018, Oxford Scholarship Online.

[61]  P. Robert,et al.  A Unifying Tool for Linear Multivariate Statistical Methods: The RV‐Coefficient , 1976 .

[62]  Matteo Magnani,et al.  Towards effective visual analytics on multiplex and multilayer networks , 2015, ArXiv.

[63]  Cristopher Moore,et al.  Community detection, link prediction, and layer interdependence in multilayer networks , 2017, Physical review. E.

[64]  Mason A. Porter,et al.  Multilayer Analysis and Visualization of Networks , 2014, J. Complex Networks.

[65]  Kevin Chen-Chuan Chang,et al.  A Comprehensive Survey of Graph Embedding: Problems, Techniques, and Applications , 2017, IEEE Transactions on Knowledge and Data Engineering.

[66]  Fosca Giannotti,et al.  Finding and Characterizing Communities in Multidimensional Networks , 2011, 2011 International Conference on Advances in Social Networks Analysis and Mining.

[67]  Vito Latora,et al.  The new challenges of multiplex networks: Measures and models , 2016, The European Physical Journal Special Topics.