Visualization and machine learning analysis of complex networks in hyperspherical space. (February 2019)

• Record Type: Journal Article
• Authors: Pereda, María; Estrada, Ernesto
• Is Part Of: Pattern recognition. Volume 86(2019:Feb.)
• Page Start: 320
• Page End: 331
• Publication Date: 2019-02
• Subjects: Networks -- Clustering algorithms -- Geometric embedding -- Communicability -- Matrix functions -- Network communities; Pattern perception -- Periodicals; Perception des structures -- Périodiques; Patroonherkenning; 006.4
• DOI: 10.1016/j.patcog.2018.09.018
• Languages: English
• ISSNs: 0031-3203

Abstract

Highlights: Networks and graphs are naturally embedded in Euclidean hyperspheres. Communicability embedding of networks/graphs reveals clusters in networks. Nonmetric multidimensional scaling allows visualization of networks in 3D communicability space. Communicability clusters of papers in a citation network reveal levels of mathematization. Communicability clusters in a gene-gene network reveal genes that co-participate in cancer and other diseases. Abstract: A complex network is a condensed representation of the relational topological framework of a complex system. A main reason for the existence of such networks is the transmission of items through the entities of these complex systems. Here, we consider a communicability function that accounts for the routes through which items flow on networks. Such a function induces a natural embedding of a network in a Euclidean high-dimensional sphere. We use one of the geometric parameters of this embedding, namely the angle between the position vectors of the nodes in the hyperspheres, to extract structural information from networks. First we propose a simple method for visualizing networks by reducing the dimensionality of the communicability space to 3-dimensional spheres. Secondly, we use clustering analysis to cluster the nodes of the networks based on their similarities in terms of their capacity to successfully deliver information through the network. After testing these approaches in benchmark networks and compare them with the most used clustering methods in networks we analyze two real-world examples. In the first, consisting of a citation network, we discover citation groups that reflect the level of mathematics used in their publications. In the second, we discover groups of genes that coparticipate in human diseases, reporting a few genes that coparticipate in cancer and other diseases. Both examples emphasize the potential of the current methodology for the discovery of new patterns in relational data.