Xavier Ouvrard

Xavier Ouvrard, Jean-Marie Le Goff, Stéphane Marchand-Maillet

Traditional verbatim browsers give back information in a linear way according to a ranking performed by a search engine that may not be optimal for the surfer. The latter may need to assess the pertinence of the information retrieved, particularly when s$\cdot$he wants to explore other facets of a multi-facetted information space. For instance, in a multimedia dataset different facets such as keywords, authors, publication category, organisations and figures can be of interest. The facet simultaneous visualisation can help to gain insights on the information retrieved and call for further searches. Facets are co-occurence networks, modeled by HyperBag-Graphs -- families of multisets -- and are in fact linked not only to the publication itself, but to any chosen reference. These references allow to navigate inside the dataset and perform visual queries. We explore here the case of scientific publications based on Arxiv searches.

Xavier Ouvrard, Jean-Marie Le Goff, Stephane Marchand-Maillet

Most networks tend to show complex and multiple relationships between entities. Networks are usually modeled by graphs or hypergraphs; nonetheless a given entity can occur many times in a relationship: this brings the need to deal with multisets instead of sets or simple edges. Diffusion processes are useful to highlight interesting parts of a network: they usually start with a stroke at one vertex and diffuse throughout the network to reach a uniform distribution. Several iterations of the process are required prior to reaching a stable solution. We propose an alternative solution to highlighting the main components of a network using a diffusion process based on exchanges: it is an iterative two-phase step exchange process. This process allows to evaluate the importance not only of the vertices but also of the regrouping level. To model the diffusion process, we extend the concept of hypergraphs that are families of sets to families of multisets, that we call hb-graphs. This version is an extended version of arXiv:1809.00190v1: the overlaps with the v1 are in black, the new content is in blue. The contributions of this extended version are: the proofs of conservation and convergence of the extracted sequences of the diffusion process, as well as the illustration of the speed of convergence and comparison to classical and modified random walks; the algorithms of the exchange-based diffusion and the modified random walk; the application to a use case based on Arxiv publications. All the figures except one have been either modified or added in this extended version to take into account the new developments.