Pretopology and Topic Modeling for Complex Systems Analysis: Application on Document Classification and Complex Network Analysis. (Prétopologie et modélisation de sujets pour l'analyse de systèmes complexes: application à la classification de documents et à l'analyse de réseaux complexes)

The work of this thesis presents the development of algorithms for document classification on the one hand, or complex network analysis on the other hand, based on pretopology, a theory that models the concept of proximity. The first work develops a framework for document clustering by combining Topic Modeling and Pretopology. Our contribution proposes using topic distributions extracted from topic modeling treatment as input for classification methods. In this approach, we investigated two aspects: determine an appropriate distance between documents by studying the relevance of Probabilistic-Based and Vector-Based Measurements and effect groupings according to several criteria using a pseudo-distance defined from pretopology. The second work introduces a general framework for modeling Complex Networks by developing a reformulation of stochastic pretopology and proposes Pretopology Cascade Model as a general model for information diffusion. In addition, we proposed an agent-based model, Textual-ABM, to analyze complex dynamic networks associated with textual information using author-topic model and introduced Textual-Homo-IC, an independent cascade model of the resemblance, in which homophily is measured based on textual content obtained by utilizing Topic Modeling.