Continuous Average Straightness in Spatial Graphs

The Straightness is a measure designed to characterize a pair of vertices in a spatial graph. It is defined as the ratio of the Euclidean distance to the graph distance between these vertices. It is often used as an average, for instance to describe the accessibility of a single vertex relatively to all the other vertices in the graph, or even to summarize the graph as a whole. In some cases, one needs to process the Straightness between not only vertices, but also any other points constituting the graph of interest. Suppose for instance that our graph represents a road network and we do not want to limit ourselves to crossroad-to-crossroad itineraries, but allow any street number to be a starting point or destination. In this situation, the standard approach consists in: 1) discretizing the graph edges, 2) processing the vertex-to-vertex Straightness considering the additional vertices resulting from this discretization, and 3) performing the appropriate average on the obtained values. However, this discrete approximation can be computationally expensive on large graphs, and its precision has not been clearly assessed. In this article, we adopt a continuous approach to average the Straightness over the edges of spatial graphs. This allows us to derive 5 distinct measures able to characterize precisely the accessibility of the whole graph, as well as individual vertices and edges. Our method is generic and could be applied to other measures designed for spatial graphs. We perform an experimental evaluation of our continuous average Straightness measures, and show how they behave differently from the traditional vertex-to-vertex ones. Moreover, we also study their discrete approximations, and show that our approach is globally less demanding in terms of both processing time and memory usage. Our R source code is publicly available under an open source license

Accuracy Measures for the Comparison of Classifiers

The selection of the best classification algorithm for a given dataset is a very widespread problem. It is also a complex one, in the sense it requires to make several important methodological choices. Among them, in this work we focus on the measure used to assess the classification performance and rank the algorithms. We present the most popular measures and discuss their properties. Despite the numerous measures proposed over the years, many of them turn out to be equivalent in this specific case, to have interpretation problems, or to be unsuitable for our purpose. Consequently, classic overall success rate or marginal rates should be preferred for this specific task.Comment: The 5th International Conference on Information Technology, amman : Jordanie (2011

Evaluation of Performance Measures for Classifiers Comparison

The selection of the best classification algorithm for a given dataset is a very widespread problem, occuring each time one has to choose a classifier to solve a real-world problem. It is also a complex task with many important methodological decisions to make. Among those, one of the most crucial is the choice of an appropriate measure in order to properly assess the classification performance and rank the algorithms. In this article, we focus on this specific task. We present the most popular measures and compare their behavior through discrimination plots. We then discuss their properties from a more theoretical perspective. It turns out several of them are equivalent for classifiers comparison purposes. Futhermore. they can also lead to interpretation problems. Among the numerous measures proposed over the years, it appears that the classical overall success rate and marginal rates are the more suitable for classifier comparison task

Opinion-Based Centrality in Multiplex Networks: A Convex Optimization Approach

Most people simultaneously belong to several distinct social networks, in which their relations can be different. They have opinions about certain topics, which they share and spread on these networks, and are influenced by the opinions of other persons. In this paper, we build upon this observation to propose a new nodal centrality measure for multiplex networks. Our measure, called Opinion centrality, is based on a stochastic model representing opinion propagation dynamics in such a network. We formulate an optimization problem consisting in maximizing the opinion of the whole network when controlling an external influence able to affect each node individually. We find a mathematical closed form of this problem, and use its solution to derive our centrality measure. According to the opinion centrality, the more a node is worth investing external influence, and the more it is central. We perform an empirical study of the proposed centrality over a toy network, as well as a collection of real-world networks. Our measure is generally negatively correlated with existing multiplex centrality measures, and highlights different types of nodes, accordingly to its definition

Comparative Evaluation of Community Detection Algorithms: A Topological Approach

Community detection is one of the most active fields in complex networks analysis, due to its potential value in practical applications. Many works inspired by different paradigms are devoted to the development of algorithmic solutions allowing to reveal the network structure in such cohesive subgroups. Comparative studies reported in the literature usually rely on a performance measure considering the community structure as a partition (Rand Index, Normalized Mutual information, etc.). However, this type of comparison neglects the topological properties of the communities. In this article, we present a comprehensive comparative study of a representative set of community detection methods, in which we adopt both types of evaluation. Community-oriented topological measures are used to qualify the communities and evaluate their deviation from the reference structure. In order to mimic real-world systems, we use artificially generated realistic networks. It turns out there is no equivalence between both approaches: a high performance does not necessarily correspond to correct topological properties, and vice-versa. They can therefore be considered as complementary, and we recommend applying both of them in order to perform a complete and accurate assessment

A community role approach to assess social capitalists visibility in the Twitter network

In the context of Twitter, social capitalists are specific users trying to increase their number of followers and interactions by any means. These users are not healthy for the service, because they are either spammers or real users flawing the notions of influence and visibility. Studying their behavior and understanding their position in Twit-ter is thus of important interest. It is also necessary to analyze how these methods effectively affect user visibility. Based on a recently proposed method allowing to identify social capitalists, we tackle both points by studying how they are organized, and how their links spread across the Twitter follower-followee network. To that aim, we consider their position in the network w.r.t. its community structure. We use the concept of community role of a node, which describes its position in a network depending on its connectiv-ity at the community level. However, the topological measures originally defined to characterize these roles consider only certain aspects of the community-related connectivity, and rely on a set of empirically fixed thresholds. We first show the limitations of these measures, before extending and generalizing them. Moreover, we use an unsupervised approach to identify the roles, in order to provide more flexibility relatively to the studied system. We then apply our method to the case of social capitalists and show they are highly visible on Twitter, due to the specific roles they hold.Comment: arXiv admin note: substantial text overlap with arXiv:1406.661

Business-oriented Analysis of a Social Network of University Students

Despites the great interest caused by social networks in Business Science, their analysis is rarely performed both in a global and systematic way in this field: most authors focus on parts of the studied network, or on a few nodes considered individually. This could be explained by the fact that practical extraction of social networks is a difficult and costly task, since the specific relational data it requires are often difficult to access and thereby expensive. One may ask if equivalent information could be extracted from less expensive individual data, i.e. data concerning single individuals instead of several ones. In this work, we try to tackle this problem through group detection. We gather both types of data from a population of students, and estimate groups separately using individual and relational data, leading to sets of clusters and communities, respectively. We found out there is no strong overlapping between them, meaning both types of data do not convey the same information in this specific context, and can therefore be considered as complementary. However, a link, even if weak, exists and appears when we identify the most discriminant attributes relatively to the communities. Implications in Business Science include community prediction using individual data.Social Networks; Business Science; Cluster Analysis; Community Detection; Community Comparison; Individual Data; Relational Data

Towards realistic artificial benchmark for community detection algorithms evaluation

Assessing the partitioning performance of community detection algorithms is one of the most important issues in complex network analysis. Artificially generated networks are often used as benchmarks for this purpose. However, previous studies showed their level of realism have a significant effect on the algorithms performance. In this study, we adopt a thorough experimental approach to tackle this problem and investigate this effect. To assess the level of realism, we use consensual network topological properties. Based on the LFR method, the most realistic generative method to date, we propose two alternative random models to replace the Configuration Model originally used in this algorithm, in order to increase its realism. Experimental results show both modifications allow generating collections of community-structured artificial networks whose topological properties are closer to those encountered in real-world networks. Moreover, the results obtained with eleven popular community identification algorithms on these benchmarks show their performance decrease on more realistic networks