Hyper-bag-graphs and their applications: Modeling, Analyzing and Visualizing Complex Networks of Co-occurrences

Abstract

Big Data calls for techniques to gain insight into the tremendous amount of data generated. This Thesis proposes a systematic approach to model using families of multisets, called hb-graphs, analyse and visualize complex co-occurrence networks, usually modelled by (hyper)graphs. Retrieving important information calls for coarsening: diffusion fits for networks and potentially requires a Laplacian tensor linked to an adjacency tensor. Revisiting systematically how diffusion can be achieved on hb-graphs, using firstly the incident matrix, which gives a baseline for the evaluation of the m-uniformisation process required for building an e-adjacency tensor for general hb-graphs, showing that any such process has an influence on the exchange-based diffusion itself; in order to improve this a layered Laplacian tensor is proposed. Two applications are then tackled, including a hb-graph framework to visually query an information space and a proposal to aggregate the rankings of reference between the different facets using the exchange-based diffusion.