Multiple Partitioning of Multiplex Signed Networks: Application to European Parliament Votes

For more than a decade, graphs have been used to model the voting behavior taking place in parliaments. However, the methods described in the literature suffer from several limitations. The two main ones are that 1) they rely on some temporal integration of the raw data, which causes some information loss, and/or 2) they identify groups of antagonistic voters, but not the context associated to their occurrence. In this article, we propose a novel method taking advantage of multiplex signed graphs to solve both these issues. It consists in first partitioning separately each layer, before grouping these partitions by similarity. We show the interest of our approach by applying it to a European Parliament dataset.Comment: Social Networks, 2020, 60, 83 - 10

Efficient Enumeration of the Optimal Solutions to the Correlation Clustering problem

According to the structural balance theory, a signed graph is considered structurally balanced when it can be partitioned into a number of modules such that positive and negative edges are respectively located inside and between the modules. In practice, real-world networks are rarely structurally balanced, though. In this case, one may want to measure the magnitude of their imbalance, and to identify the set of edges causing this imbalance. The correlation clustering (CC) problem precisely consists in looking for the signed graph partition having the least imbalance. Recently, it has been shown that the space of the optimal solutions of the CC problem can be constituted of numerous and diverse optimal solutions. Yet, this space is difficult to explore, as the CC problem is NP-hard, and exact approaches do not scale well even when looking for a single optimal solution. To alleviate this issue, in this work we propose an efficient enumeration method allowing to retrieve the complete space of optimal solutions of the CC problem. It combines an exhaustive enumeration strategy with neighborhoods of varying sizes, to achieve computational effectiveness. Results obtained for middle-sized networks confirm the usefulness of our method

Multiplicité dans le partitionnement de graphes signés

According to the structural balance theory, a signed graph is considered structurally balanced when it can be partitioned into a number of modules such that positive edges are located inside the modules and negatives ones are in-between them. In practice, real-world networks are rarely perfectly balanced. When it is not the case, one wants to measure the magnitude of the imbalance and to identify the set of edges related to the network imbalance. The Correlation Clustering (CC) problem is precisely defined as finding the partition with minimal imbalance. Signed graph partitioning is an important task, which has many applications, as finding a balanced partition helps understanding the system modeled by the graph. However, the standard approach used in the literature is to find a single partition and focus the rest of the analysis on it, as if it was sufficient to fully characterize the studied system. Yet, it may not reflect the meso-structure of the network, and one may need to seek for other partitions to build a better picture. Although this need to look for multiplicity is extremely important from the end user's perspective, only a very few works took it into consideration in their analysis, up to now. In this thesis, we want to relax this traditional single-partition assumption to allow searching for multiple partitions in two separate situations. The first one arises in the context of signed multiplex networks. All traditional approaches proposed to partition multiplex networks in general are based on the single-partition assumption. To overcome this limitation, we propose a new partitioning method that integrates a meta-clustering process before merging the partitions of individual layers, which allows identifying structurally similar layers. The second situation is specific to the CC problem. When solving an instance of such problem, several or even many optimal partitions may coexist. If multiple optimal partitions coexist, one can then wonder how different/diverse they are. Put differently, we want to know what we loose when considering only one partition, while there might be multiple ones. In order to answer these questions, one should ideally enumerate completely the space of optimal partitions, and perform its analysis. To this end, we propose a new efficient solution space enumeration method and a cluster analysis-based framework in order to first enumerate the space of optimal partitions and then empirically study such space. Lastly, each of these previous situations requires to compute the similarity between partitions. In the context of graph partitioning, this task can be done through a so-called external evaluation measure. However, there exist many such measures, each having different characteristics. This makes it challenging to select the most appropriate for a given situation for the end user. To this end, we propose a new empirical evaluation framework in order to produce results that end users can easily interpret. For a collection of candidate measures, it first consists in describing their behavior by computing them for a generated dataset of parametric partitions, obtained by applying a set of predefined parametric partition transformations. Second, our framework characterizes the measures in terms of how they are affected by these parameters and transformations.Selon la théorie de l'équilibre structural, un graphe signé est structurellement équilibré s’il peut être partitionné en sous-groupes mutuellement hostiles (i.e. reliés seulement par des liens négatifs) tout en exhibant une solidarité interne (i.e. contenant uniquement des liens positifs). Mais un réseau réel (i.e. un graphe représentant un système du monde réel) est rarement parfaitement équilibré : on trouvera quelques liens positifs entre les groupes et/ou quelques liens négatifs à l’intérieur de certains groupes. L’un des défis du domaine est de quantifier le niveau de déséquilibre d’un tel réseau et d'identifier les liens qui causent ce déséquilibre. Le problème Correlation Clustering (CC) se définit précisément par l'obtention d'une partition possédant un déséquilibre minimal. Le partitionnement de graphes signés constitue une tâche importante du point de vue applicatif, étant donné que trouver une partition équilibrée aide à comprendre le système modélisé par le graphe signé. Cependant, l'approche standard dans la littérature se contente de chercher une seule partition, comme si elle caractérisait suffisamment le système étudié. Or, on peut avoir besoin de plusieurs partitions pour construire une image plus juste du système étudié. Même si cette notion de la multiplicité est extrêmement important du point de vue des utilisateurs finaux, elle a été très peu abordée dans la littérature. Dans cette thèse, on veut relaxer l'hypothèse de partition unique pour en chercher plusieurs, et ce dans deux situations séparées. La première concerne les graphes multiplexes signés. Toutes les approches traditionnelles proposées pour les graphes multiplexes produisent une seule partition à la fin. Pour pallier ce problème, nous proposons une nouvelle approche qui intègre un processus de clustering avant de fusionner les couches individuelles, ce qui permet de regrouper les couches structurellement similaires. La deuxième situation est spécifique au problème CC. Quand on résout une instance de ce problème, plusieurs partitions optimales peuvent coexister. La question qui se pose est de savoir ce qu'on perd, si on considère une seule partition optimale, alors qu'il en existe plusieurs. Idéalement, il faut les énumérer toutes avant de faire une analyse concluante. Pour ce faire, on propose une nouvelle méthode d'énumération et un framework basé sur l'analyse de clustering afin de d'abord complètement énumérer l'espace des partitions optimales, puis étudier empiriquement un tel espace. Dans les deux situations décrites ci-dessus, mesurer la similarité entre deux partitions est un point essentiel. Pourtant, il n'existe pas une définition de la meilleure mesure pour cela, étant donné que toute définition de la similarité est subjective et dépend notamment de l'application considérée. En conséquence, de nombreuses mesures ont été décrites dans la littérature. Cependant, l'abondance de mesures de similarité est une limitation plutôt qu'un avantage, car la sélection de la mesure la plus appropriée pour une application donnée devient un défi pour les utilisateurs finaux. Pour pallier ce problème, nous proposons un nouveau framework. Celui-ci prend en compte plusieurs paramètres liés au partitionnement, et évalue statistiquement les mesures dans plusieurs scénarios de partitionnement à travers ces paramètres, via l'analyse de régression

MultiNetVotes - Multiple Partitioning of Multiplex Signed Networks: Application to European Parliament Votes

This set of R scripts was designed to analyze the European Parliament votes through a multiplex network-based approach. See the bibliographic reference indicated in the readme file for more details. Our tool was applied to data representing the activity of the members of the European Parliament (MEPs) during the 7th term (from June 2009 to June 2014), as described in [AFL'19]. The raw data describing this activity were retrieved from the It's Your Parliament website. There were some minor issues with these data, which we had to correct: some MEPs were represented twice, some profiles were incomplete, the policy domains were not defined for all vote texts, etc. These cleaned data are available on FigShare (see readme file)

Analysis of Roll-Calls in the European Parliament by Multiple Partitioning of Multiplex Signed Networks

International audienceFor more than a decade, graphs have been used to model the voting behavior taking place in parliaments. However, the methods described in the literature suffer from several limitations. The two main ones are that 1) they rely on some temporal integration of the raw data, which causes some information loss; and/or 2) they identify groups of antagonistic voters, but not the context associated to their occurrence. In this article, we propose a novel method taking advantage of multiplex signed graphs to solve both these issues. It consists in first partitioning separately each layer, before grouping these partitions by similarity. We show the interest of our approach by applying it to a European Parliament dataset

Multiplicity in Signed Graph Partitioning

International audienc

Multiple Optimal Solutions but Single Search: A Study of the Correlation Clustering Problem

Abstract, Communication oraleNational audienc