Vincent Levorato

Detection of communities in directed networks based on strongly p-connected components

A lot of algorithms in communities detection have been proposed particularly for undirected networks. As methods to find communities in directed networks are few, our contribution is to propose a method based on strongly and unilaterally connected components, and more specifically on strongly p-connected components in directed graphs. The result is a clustering of nodes giving good results in generated graphs according to several clustering evaluation measures, and which practical time complexity remains acceptable.

Abstract geometrical computation 8: Small machines, accumulations & rationality

In the context of abstract geometrical computation, computing with colored line segments, we study the possibility of having an accumulation with small signal machines, ie, signal machines having only a very limited number of distinct speeds. The cases of 2 and 4 speeds are trivial: we provide a proof that no machine can produce an accumulation in the case of 2 speeds and exhibit an accumulation with 4 speeds. The main result is the twofold case of 3 speeds. On the one hand, we prove that accumulations cannot happen when all ratios between speeds and all ratios between initial distances are rational. On the other hand, we provide examples of an accumulation in the case of an irrational ratio between 2 speeds and in the case of an irrational ratio between two distances in the initial configuration. This dichotomy is explained by the presence of a phenomenon computing Euclids algorithm (gcd): it stops if and only if its input is commensurate (ie, of rational ratio).

QASSIT: A Pretopological Framework for the Automatic Construction of Lexical Taxonomies from Raw Texts

This paper presents our participation to the SemEval Task-17, related to “Taxonomy Extraction Evaluation” (Bordea et al., 2015). We propose a new methodology for semi-supervised and auto-supervised acquisition of lexical taxonomies from raw texts. Our approach is based on the theory of pretopology that offers a powerful formalism to model subsumption relations and transforms a list of terms into a structured term space by combining different discriminant criteria. In order to reach a good pretopological space, we define the Learning Pretopological Spaces method that learns a parameterized space by using an evolutionary strategy.

Generalized Percolation Processes Using Pretopology Theory

We propose in this paper a generalization of percolation processes in Z2 using the pretopology theory. We formalize the notion of neighborhood by extending it to the concept of proximity, expressing different types of connections that may exist between the elements of a population. A modeling and simulation of forest fire using this approach shows the efficiency of this formalism to provide a realistic and powerful modeling of complex systems.

Core Decomposition in Directed Networks: Kernelization and Strong Connectivity

In this paper, we propose a method allowing decomposition of directed networks into cores, which final objective is the detection of communities.We based our approach on the fact that a community should be composed of elements having communication in both directions. Therefore, we propose a method based on digraph kernelization and strongly p-connected components. By identifying cores, one can use based-centers clustering methods to generate full communities. Some experiments have been made on three real-world networks, and have been evaluated using the V-Measure, having a more precise analysis through its two sub-measures: homogeneity and completeness. Our work proposes different directions about the use of kernelization into structure analysis, and strong connectivity concept as an alternative to modularity optimization.