Nejat Arinik, Vincent Labatut, Rosa Figueiredo
In the context of cluster analysis and graph partitioning, many external evaluation measures have been proposed in the literature to compare two partitions of the same set. This makes the task of selecting the most appropriate measure for a given situation a challenge for the end user. However, this issue is overlooked in the literature. Researchers tend to follow tradition and use the standard measures of their field, although they often became standard only because previous researchers started consistently using them. In this work, we propose a new empirical evaluation framework to solve this issue, and help the end user selecting an appropriate measure for their application. For a collection of candidate measures, it first consists in describing their behavior by computing them for a generated dataset of partitions, obtained by applying a set of predefined parametric partition transformations. Second, our framework performs a regression analysis to characterize the measures in terms of how they are affected by these parameters and transformations. This allows both describing and comparing the measures. Our approach is not tied to any specific measure or application, so it can be applied to any situation. We illustrate its relevance by applying it to a selection of standard measures, and show how it can be put in practice through two concrete use cases.
Nejat Arinik, Rosa Figueiredo, Vincent Labatut
In order to study real-world systems, many applied works model them through signed graphs, i.e. graphs whose edges are labeled as either positive or negative. Such a graph is considered as structurally balanced when it can be partitioned into a number of modules, such that positive (resp. negative) edges are located inside (resp. in-between) the modules. When it is not the case, authors look for the closest partition to such balance, a problem called Correlation Clustering (CC). Due to the complexity of the CC problem, the standard approach is to find a single optimal partition and stick to it, even if other optimal or high scoring solutions possibly exist. In this work, we study the space of optimal solutions of the CC problem, on a collection of synthetic complete graphs. We show empirically that under certain conditions, there can be many optimal partitions of a signed graph. Some of these are very different and thus provide distinct perspectives on the system, as illustrated on a small real-world graph. This is an important result, as it implies that one may have to find several, if not all, optimal solutions of the CC problem, in order to properly study the considered system.
Nejat Arinik, Rosa Figueiredo, Vincent Labatut
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.
Nejat Arinik, Rosa Figueiredo, Vincent Labatut
In a signed graph, each link is labeled with either a positive or a negative sign. This is particularly appropriate to model polarized systems. Such a graph can be characterized through the notion of structural balance, which relies on the partitioning of the graph into internally solidary but mutually hostile subgroups. In this work, we show that signed graphs can be used to model and understand voting behavior. We take advantage of data from the European Parliament to confront two variants of structural balance, and illustrate how their use can help better understanding the studied system.
Nejat Arinik, Roberto Interdonato, Mathieu Roche, Maguelonne Teisseire
In the context of Epidemic Intelligence, many Event-Based Surveillance (EBS) systems have been proposed in the literature to promote the early identification and characterization of potential health threats from online sources of any nature. Each EBS system has its own surveillance definitions and priorities, therefore this makes the task of selecting the most appropriate EBS system for a given situation a challenge for end-users. In this work, we propose a new evaluation framework to address this issue. It first transforms the raw input epidemiological event data into a set of normalized events with multi-granularity, then conducts a descriptive retrospective analysis based on four evaluation objectives: spatial, temporal, thematic and source analysis. We illustrate its relevance by applying it to an Avian Influenza dataset collected by a selection of EBS systems, and show how our framework allows identifying their strengths and drawbacks in terms of epidemic surveillance.
Nejat Arinik, Vincent Labatut, Rosa Figueiredo
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.
Noé Cecillon, Vincent Labatut, Richard Dufour, Nejat Arınık
Graphs are ubiquitous for modeling complex systems involving structured data and relationships. Consequently, graph representation learning, which aims to automatically learn low-dimensional representations of graphs, has drawn a lot of attention in recent years. The overwhelming majority of existing methods handle unsigned graphs. However, signed graphs appear in an increasing number of application domains to model systems involving two types of opposed relationships. Several authors took an interest in signed graphs and proposed methods for providing vertex-level representations, but only one exists for whole-graph representations, and it can handle only fully connected graphs. In this article, we tackle this issue by proposing two approaches to learning whole-graph representations of general signed graphs. The first is a SG2V, a signed generalization of the whole-graph embedding method Graph2vec that relies on a modification of the Weisfeiler--Lehman relabelling procedure. The second one is WSGCN, a whole-graph generalization of the signed vertex embedding method SGCN that relies on the introduction of master nodes into the GCN. We propose several variants of both these approaches. A bottleneck in the development of whole-graph-oriented methods is the lack of data. We constitute a benchmark composed of three collections of signed graphs with corresponding ground truths. We assess our methods on this benchmark, and our results show that the signed whole-graph methods learn better representations for this task. Overall, the baseline obtains an F-measure score of 58.57, when SG2V and WSGCN reach 73.01 and 81.20, respectively. Our source code and benchmark dataset are both publicly available online.