Federica Baccini (University of Siena)

When: Nov 3rd, 2021 – 11:00 – 11:45 AM

Where: Google meet link

Description

In this talk, a linear algebra based set up for computing the barycenter of multiplex similarity networks will be discussed. Multiplex networks are mathematical objects that allow to describe multiple types of relations among a fixed set of objects. Given a multiplex network, one might be interested in detecting communities and measuring the relevance of each relation type in the determination of clusters. A convenient approach could be that of collapsing the multiplex structure into a unique representative graph (network barycenter), and then to perform the desired analysis on it. In this seminar, we propose the use of weighted matrix means to compute the barycenter of a multiplex similarity network. We first give insights of some matrix spaces that ensure that the matrix mean of a multiplex similarity network is well defined. Then, we suggest a choice for assigning weights to each layer of similarity, based on the idea that the more a layer is similar to the others, the more it is representative of the whole multilayer structure.