Arnaud Martin

Arnaud Martin

Most questionnaires offer ordered responses whose order is poorly studied via belief functions. In this paper, we study the consequences of a frame of discernment consisting of ordered elements on belief functions. This leads us to redefine the power space and the union of ordered elements for the disjunctive combination. We also study distances on ordered elements and their use. In particular, from a membership function, we redefine the cardinality of the intersection of ordered elements, considering them fuzzy.

Arthur Hoarau, Vincent Lemaire, Arnaud Martin et al.

Recent studies in active learning, particularly in uncertainty sampling, have focused on the decomposition of model uncertainty into reducible and irreducible uncertainties. In this paper, the aim is to simplify the computational process while eliminating the dependence on observations. Crucially, the inherent uncertainty in the labels is considered, the uncertainty of the oracles. Two strategies are proposed, sampling by Klir uncertainty, which tackles the exploration-exploitation dilemma, and sampling by evidential epistemic uncertainty, which extends the concept of reducible uncertainty within the evidential framework, both using the theory of belief functions. Experimental results in active learning demonstrate that our proposed method can outperform uncertainty sampling.

Constance Thierry, Arnaud Martin, Jean-Christophe Dubois et al.

Crowdsourcing is the outsourcing of tasks to a crowd of contributors on a dedicated platform. The crowd on these platforms is very diversified and includes various profiles of contributors which generates data of uneven quality. However, majority voting, which is the aggregating method commonly used in platforms, gives equal weight to each contribution. To overcome this problem, we propose a method, MONITOR, which estimates the contributor's profile and aggregates the collected data by taking into account their possible imperfections thanks to the theory of belief functions. To do so, MONITOR starts by estimating the profile of the contributor through his qualification for the task and his behavior.Crowdsourcing campaigns have been carried out to collect the necessary data to test MONITOR on real data in order to compare it to existing approaches. The results of the experiments show that thanks to the use of the MONITOR method, we obtain a better rate of correct answer after aggregation of the contributions compared to the majority voting. Our contributions in this article are for the first time the proposal of a model that takes into account both the qualification of the contributor and his behavior in the estimation of his profile. For the second one, the weakening and the aggregation of the answers according to the estimated profiles.

Constance Thierry, Jean-Christophe Dubois, Yolande Le Gall et al.

Crowdsourcing is defined as the outsourcing of tasks to a crowd of contributors. The crowd is very diverse on these platforms and includes malicious contributors attracted by the remuneration of tasks and not conscientiously performing them. It is essential to identify these contributors in order to avoid considering their responses. As not all contributors have the same aptitude for a task, it seems appropriate to give weight to their answers according to their qualifications. This paper, published at the ICTAI 2019 conference, proposes a method, MONITOR, for estimating the profile of the contributor and aggregating the responses using belief function theory.

Siwar Jendoubi, Arnaud Martin

The Viral Marketing is a relatively new form of marketing that exploits social networks to promote a brand, a product, etc. The idea behind it is to find a set of influencers on the network that can trigger a large cascade of propagation and adoptions. In this paper, we will introduce an evidential opinion-based influence maximization model for viral marketing. Besides, our approach tackles three opinions based scenarios for viral marketing in the real world. The first scenario concerns influencers who have a positive opinion about the product. The second scenario deals with influencers who have a positive opinion about the product and produce effects on users who also have a positive opinion. The third scenario involves influence users who have a positive opinion about the product and produce effects on the negative opinion of other users concerning the product in question. Next, we proposed six influence measures, two for each scenario. We also use an influence maximization model that the set of detected influencers for each scenario. Finally, we show the performance of the proposed model with each influence measure through some experiments conducted on a generated dataset and a real world dataset collected from Twitter.

Jean-Christophe Dubois, Laetitia Gros, Mouloud Kharoune et al.

Crowdsourcing platforms enable companies to propose tasks to a large crowd of users. The workers receive a compensation for their work according to the serious of the tasks they managed to accomplish. The evaluation of the quality of responses obtained from the crowd remains one of the most important problems in this context. Several methods have been proposed to estimate the expertise level of crowd workers. We propose an innovative measure of expertise assuming that we possess a dataset with an objective comparison of the items concerned. Our method is based on the definition of four factors with the theory of belief functions. We compare our method to the Fagin distance on a dataset from a real experiment, where users have to assess the quality of some audio recordings. Then, we propose to fuse both the Fagin distance and our expertise measure.

Constance Thierry, Jean-Christophe Dubois, Yolande Le Gall et al.

The crowdsourcing consists in the externalisation of tasks to a crowd of people remunerated to execute this ones. The crowd, usually diversified, can include users without qualification and/or motivation for the tasks. In this paper we will introduce a new method of user expertise modelization in the crowdsourcing platforms based on the theory of belief functions in order to identify serious and qualificated users.

Kuang Zhou, Arnaud Martin, Quan Pan

The theory of belief functions is widely used for data from multiple sources. Different evidence combination rules have been proposed in this framework according to the properties of the sources to combine. However, most of these combination rules are not efficient when there are a large number of sources. This is due to either the complexity or the existence of an absorbing element such as the total conflict mass function for the conjunctive based rules when applied on unreliable evidence. In this paper, based on the assumption that the majority of sources are reliable, a combination rule for a large number of sources is proposed using a simple idea: the more common ideas the sources share, the more reliable these sources are supposed to be. This rule is adaptable for aggregating a large number of sources which may not all be reliable. It will keep the spirit of the conjunctive rule to reinforce the belief on the focal elements with which the sources are in agreement. The mass on the emptyset will be kept as an indicator of the conflict. The proposed rule, called LNS-CR (Conjunctive combinationRule for a Large Number of Sources), is evaluated on synthetic mass functions. The experimental results verify that the rule can be effectively used to combine a large number of mass functions and to elicit the major opinion.

Kuang Zhou, Quan Pan, Arnaud Martin

Credal partitions in the framework of belief functions can give us a better understanding of the analyzed data set. In order to find credal community structure in graph data sets, in this paper, we propose a novel evidential community detection algorithm based on density peaks (EDPC). Two new metrics, the local density $ρ$ and the minimum dissimi-larity $δ$, are first defined for each node in the graph. Then the nodes with both higher $ρ$ and $δ$ values are identified as community centers. Finally, the remaing nodes are assigned with corresponding community labels through a simple two-step evidential label propagation strategy. The membership of each node is described in the form of basic belief assignments , which can well express the uncertainty included in the community structure of the graph. The experiments demonstrate the effectiveness of the proposed method on real-world networks.

Manel Chehibi, Mouna Chebbah, Arnaud Martin

Online social networks are more and more studied. The links between users of a social network are important and have to be well qualified in order to detect communities and find influencers for example. In this paper, we present an approach based on the theory of belief functions to estimate the degrees of cognitive independence between users in a social network. We experiment the proposed method on a large amount of data gathered from the Twitter social network.

Arnaud Martin

In Information fusion, the conflict is an important concept. Indeed, combining several imperfect experts or sources allows conflict. In the theory of belief functions, this notion has been discussed a lot. The mass appearing on the empty set during the conjunctive combination rule is generally considered as conflict, but that is not really a conflict. Some measures of conflict have been proposed and some approaches have been proposed in order to manage this conflict or to decide with conflicting mass functions. We recall in this chapter some of them and we propose a discussion to consider the conflict in information fusion with the theory of belief functions.

Yiru Zhang, Tassadit Bouadi, Arnaud Martin

Facing an unknown situation, a person may not be able to firmly elicit his/her preferences over different alternatives, so he/she tends to express uncertain preferences. Given a community of different persons expressing their preferences over certain alternatives under uncertainty, to get a collective representative opinion of the whole community, a preference fusion process is required. The aim of this work is to propose a preference fusion method that copes with uncertainty and escape from the Condorcet paradox. To model preferences under uncertainty, we propose to develop a model of preferences based on belief function theory that accurately describes and captures the uncertainty associated with individual or collective preferences. This work improves and extends the previous results. This work improves and extends the contribution presented in a previous work. The benefits of our contribution are twofold. On the one hand, we propose a qualitative and expressive preference modeling strategy based on belief-function theory which scales better with the number of sources. On the other hand, we propose an incremental distance-based algorithm (using Jousselme distance) for the construction of the collective preference order to avoid the Condorcet Paradox.

Na Li, Arnaud Martin, Rémi Estival

Detection of surface water in natural environment via multi-spectral imagery has been widely utilized in many fields, such land cover identification. However, due to the similarity of the spectra of water bodies, built-up areas, approaches based on high-resolution satellites sometimes confuse these features. A popular direction to detect water is spectral index, often requiring the ground truth to find appropriate thresholds manually. As for traditional machine learning methods, they identify water merely via differences of spectra of various land covers, without taking specific properties of spectral reflection into account. In this paper, we propose an automatic approach to detect water bodies based on Dempster-Shafer theory, combining supervised learning with specific property of water in spectral band in a fully unsupervised context. The benefits of our approach are twofold. On the one hand, it performs well in mapping principle water bodies, including little streams and branches. On the other hand, it labels all objects usually confused with water as `ignorance', including half-dry watery areas, built-up areas and semi-transparent clouds and shadows. `Ignorance' indicates not only limitations of the spectral properties of water and supervised learning itself but insufficiency of information from multi-spectral bands as well, providing valuable information for further land cover classification.

Salma Ben Dhaou, Kuang Zhou, Mouloud Kharoune et al.

Nowadays, there are many approaches designed for the task of detecting communities in social networks. Among them, some methods only consider the topological graph structure, while others take use of both the graph structure and the node attributes. In real-world networks, there are many uncertain and noisy attributes in the graph. In this paper, we will present how we detect communities in graphs with uncertain attributes in the first step. The numerical, probabilistic as well as evidential attributes are generated according to the graph structure. In the second step, some noise will be added to the attributes. We perform experiments on graphs with different types of attributes and compare the detection results in terms of the Normalized Mutual Information (NMI) values. The experimental results show that the clustering with evidential attributes gives better results comparing to those with probabilistic and numerical attributes. This illustrates the advantages of evidential attributes.

Kuang Zhou, Arnaud Martin, Quan Pan

The theory of belief functions is an effective tool to deal with the multiple uncertain information. In recent years, many evidence combination rules have been proposed in this framework, such as the conjunctive rule, the cautious rule, the PCR (Proportional Conflict Redistribution) rules and so on. These rules can be adopted for different types of sources. However, most of these rules are not applicable when the number of sources is large. This is due to either the complexity or the existence of an absorbing element (such as the total conflict mass function for the conjunctive-based rules when applied on unreliable evidence). In this paper, based on the assumption that the majority of sources are reliable, a combination rule for a large number of sources, named LNS (stands for Large Number of Sources), is proposed on the basis of a simple idea: the more common ideas one source shares with others, the morereliable the source is. This rule is adaptable for aggregating a large number of sources among which some are unreliable. It will keep the spirit of the conjunctive rule to reinforce the belief on the focal elements with which the sources are in agreement. The mass on the empty set will be kept as an indicator of the conflict. Moreover, it can be used to elicit the major opinion among the experts. The experimental results on synthetic mass functionsverify that the rule can be effectively used to combine a large number of mass functions and to elicit the major opinion.

Siwar Jendoubi, Arnaud Martin

The influence maximization is the problem of finding a set of social network users, called influencers, that can trigger a large cascade of propagation. Influencers are very beneficial to make a marketing campaign goes viral through social networks for example. In this paper, we propose an influence measure that combines many influence indicators. Besides, we consider the reliability of each influence indicator and we present a distance-based process that allows to estimate the reliability of each indicator. The proposed measure is defined under the framework of the theory of belief functions. Furthermore, the reliability-based influence measure is used with an influence maximization model to select a set of users that are able to maximize the influence in the network. Finally, we present a set of experiments on a dataset collected from Twitter. These experiments show the performance of the proposed solution in detecting social influencers with good quality.

Siwar Jendoubi, Arnaud Martin, Ludovic Liétard et al.

Social messages classification is a research domain that has attracted the attention of many researchers in these last years. Indeed, the social message is different from ordinary text because it has some special characteristics like its shortness. Then the development of new approaches for the processing of the social message is now essential to make its classification more efficient. In this paper, we are mainly interested in the classification of social messages based on their spreading on online social networks (OSN). We proposed a new distance metric based on the Dynamic Time Warping distance and we use it with the probabilistic and the evidential k Nearest Neighbors (k-NN) classifiers to classify propagation networks (PrNets) of messages. The propagation network is a directed acyclic graph (DAG) that is used to record propagation traces of the message, the traversed links and their types. We tested the proposed metric with the chosen k-NN classifiers on real world propagation traces that were collected from Twitter social network and we got good classification accuracies.

Hosna Ouni, Arnaud Martin, Laetitia Gros et al.

Crowdsourcing, a major economic issue, is the fact that the firm outsources internal task to the crowd. It is a form of digital subcontracting for the general public. The evaluation of the participants work quality is a major issue in crowdsourcing. Indeed, contributions must be controlled to ensure the effectiveness and relevance of the campaign. We are particularly interested in small, fast and not automatable tasks. Several methods have been proposed to solve this problem, but they are applicable when the "golden truth" is not always known. This work has the particularity to propose a method for calculating the degree of expertise in the presence of gold data in crowdsourcing. This method is based on the belief function theory and proposes a structuring of data using graphs. The proposed approach will be assessed and applied to the data.

Siwar Jendoubi, Arnaud Martin, Ludovic Liétard et al.

In this paper, we propose a new data based model for influence maximization in online social networks. We use the theory of belief functions to overcome the data imperfection problem. Besides, the proposed model searches to detect influencer users that adopt a positive opinion about the product, the idea, etc, to be propagated. Moreover, we present some experiments to show the performance of our model.

Amal Ben Rjab, Mouloud Kharoune, Zoltan Miklos et al.

Crowdsourcing platforms enable to propose simple human intelligence tasks to a large number of participants who realise these tasks. The workers often receive a small amount of money or the platforms include some other incentive mechanisms, for example they can increase the workers reputation score, if they complete the tasks correctly. We address the problem of identifying experts among participants, that is, workers, who tend to answer the questions correctly. Knowing who are the reliable workers could improve the quality of knowledge one can extract from responses. As opposed to other works in the literature, we assume that participants can give partial or incomplete responses, in case they are not sure that their answers are correct. We model such partial or incomplete responses with the help of belief functions, and we derive a measure that characterizes the expertise level of each participant. This measure is based on precise and exactitude degrees that represent two parts of the expertise level. The precision degree reflects the reliability level of the participants and the exactitude degree reflects the knowledge level of the participants. We also analyze our model through simulation and demonstrate that our richer model can lead to more reliable identification of experts.

Kuang Zhou, Arnaud Martin, Quan Pan

In the task of community detection, there often exists some useful prior information. In this paper, a Semi-supervised clustering approach using a new Evidential Label Propagation strategy (SELP) is proposed to incorporate the domain knowledge into the community detection model. The main advantage of SELP is that it can take limited supervised knowledge to guide the detection process. The prior information of community labels is expressed in the form of mass functions initially. Then a new evidential label propagation rule is adopted to propagate the labels from labeled data to unlabeled ones. The outliers can be identified to be in a special class. The experimental results demonstrate the effectiveness of SELP.

Kuang Zhou, Arnaud Martin, Quan Pan et al.

Community detection has attracted considerable attention crossing many areas as it can be used for discovering the structure and features of complex networks. With the increasing size of social networks in real world, community detection approaches should be fast and accurate. The Label Propagation Algorithm (LPA) is known to be one of the near-linear solutions and benefits of easy implementation, thus it forms a good basis for efficient community detection methods. In this paper, we extend the update rule and propagation criterion of LPA in the framework of belief functions. A new community detection approach, called Evidential Label Propagation (ELP), is proposed as an enhanced version of conventional LPA. The node influence is first defined to guide the propagation process. The plausibility is used to determine the domain label of each node. The update order of nodes is discussed to improve the robustness of the method. ELP algorithm will converge after the domain labels of all the nodes become unchanged. The mass assignments are calculated finally as memberships of nodes. The overlapping nodes and outliers can be detected simultaneously through the proposed method. The experimental results demonstrate the effectiveness of ELP.

Kuang Zhou, Arnaud Martin, Quan Pan

One difficulty faced in knowledge engineering for Bayesian Network (BN) is the quan-tification step where the Conditional Probability Tables (CPTs) are determined. The number of parameters included in CPTs increases exponentially with the number of parent variables. The most common solution is the application of the so-called canonical gates. The Noisy-OR (NOR) gate, which takes advantage of the independence of causal interactions, provides a logarithmic reduction of the number of parameters required to specify a CPT. In this paper, an extension of NOR model based on the theory of belief functions, named Belief Noisy-OR (BNOR), is proposed. BNOR is capable of dealing with both aleatory and epistemic uncertainty of the network. Compared with NOR, more rich information which is of great value for making decisions can be got when the available knowledge is uncertain. Specially, when there is no epistemic uncertainty, BNOR degrades into NOR. Additionally, different structures of BNOR are presented in this paper in order to meet various needs of engineers. The application of BNOR model on the reliability evaluation problem of networked systems demonstrates its effectiveness.

Kuang Zhou, Arnaud Martin, Quan Pan et al.

In this work, a new prototype-based clustering method named Evidential C-Medoids (ECMdd), which belongs to the family of medoid-based clustering for proximity data, is proposed as an extension of Fuzzy C-Medoids (FCMdd) on the theoretical framework of belief functions. In the application of FCMdd and original ECMdd, a single medoid (prototype), which is supposed to belong to the object set, is utilized to represent one class. For the sake of clarity, this kind of ECMdd using a single medoid is denoted by sECMdd. In real clustering applications, using only one pattern to capture or interpret a class may not adequately model different types of group structure and hence limits the clustering performance. In order to address this problem, a variation of ECMdd using multiple weighted medoids, denoted by wECMdd, is presented. Unlike sECMdd, in wECMdd objects in each cluster carry various weights describing their degree of representativeness for that class. This mechanism enables each class to be represented by more than one object. Experimental results in synthetic and real data sets clearly demonstrate the superiority of sECMdd and wECMdd. Moreover, the clustering results by wECMdd can provide richer information for the inner structure of the detected classes with the help of prototype weights.

Zhun-Ga Liu, Quan Pan, Jean Dezert et al.

In classification of incomplete pattern, the missing values can either play a crucial role in the class determination, or have only little influence (or eventually none) on the classification results according to the context. We propose a credal classification method for incomplete pattern with adaptive imputation of missing values based on belief function theory. At first, we try to classify the object (incomplete pattern) based only on the available attribute values. As underlying principle, we assume that the missing information is not crucial for the classification if a specific class for the object can be found using only the available information. In this case, the object is committed to this particular class. However, if the object cannot be classified without ambiguity, it means that the missing values play a main role for achieving an accurate classification. In this case, the missing values will be imputed based on the K-nearest neighbor (K-NN) and self-organizing map (SOM) techniques, and the edited pattern with the imputation is then classified. The (original or edited) pattern is respectively classified according to each training class, and the classification results represented by basic belief assignments are fused with proper combination rules for making the credal classification. The object is allowed to belong with different masses of belief to the specific classes and meta-classes (which are particular disjunctions of several single classes). The credal classification captures well the uncertainty and imprecision of classification, and reduces effectively the rate of misclassifications thanks to the introduction of meta-classes. The effectiveness of the proposed method with respect to other classical methods is demonstrated based on several experiments using artificial and real data sets.

Kuang Zhou, Arnaud Martin, Quan Pan et al.

In real clustering applications, proximity data, in which only pairwise similarities or dissimilarities are known, is more general than object data, in which each pattern is described explicitly by a list of attributes. Medoid-based clustering algorithms, which assume the prototypes of classes are objects, are of great value for partitioning relational data sets. In this paper a new prototype-based clustering method, named Evidential C-Medoids (ECMdd), which is an extension of Fuzzy C-Medoids (FCMdd) on the theoretical framework of belief functions is proposed. In ECMdd, medoids are utilized as the prototypes to represent the detected classes, including specific classes and imprecise classes. Specific classes are for the data which are distinctly far from the prototypes of other classes, while imprecise classes accept the objects that may be close to the prototypes of more than one class. This soft decision mechanism could make the clustering results more cautious and reduce the misclassification rates. Experiments in synthetic and real data sets are used to illustrate the performance of ECMdd. The results show that ECMdd could capture well the uncertainty in the internal data structure. Moreover, it is more robust to the initializations compared with FCMdd.

Mouna Chebbah, Arnaud Martin, Boutheina Ben Yaghlane

The theory of belief functions manages uncertainty and also proposes a set of combination rules to aggregate opinions of several sources. Some combination rules mix evidential information where sources are independent; other rules are suited to combine evidential information held by dependent sources. In this paper we have two main contributions: First we suggest a method to quantify sources' degree of independence that may guide the choice of the more appropriate set of combination rules. Second, we propose a new combination rule that takes consideration of sources' degree of independence. The proposed method is illustrated on generated mass functions.

Amira Essaid, Arnaud Martin, Grégory Smits et al.

Belief function theory provides a flexible way to combine information provided by different sources. This combination is usually followed by a decision making which can be handled by a range of decision rules. Some rules help to choose the most likely hypothesis. Others allow that a decision is made on a set of hypotheses. In [6], we proposed a decision rule based on a distance measure. First, in this paper, we aim to demonstrate that our proposed decision rule is a particular case of the rule proposed in [4]. Second, we give experiments showing that our rule is able to decide on a set of hypotheses. Some experiments are handled on a set of mass functions generated randomly, others on real databases.

Dorra Attiaoui, Pierre-Emmanuel Doré, Arnaud Martin et al.

Defining and modeling the relation of inclusion between continuous belief function may be considered as an important operation in order to study their behaviors. Within this paper we will propose and present two forms of inclusion: The strict and the partial one. In order to develop this relation, we will study the case of consonant belief function. To do so, we will simulate normal distributions allowing us to model and analyze these relations. Based on that, we will determine the parameters influencing and characterizing the two forms of inclusion.

Amira Essaid, Arnaud Martin, Grégory Smits et al.

Considering the high heterogeneity of the ontologies pub-lished on the web, ontology matching is a crucial issue whose aim is to establish links between an entity of a source ontology and one or several entities from a target ontology. Perfectible similarity measures, consid-ered as sources of information, are combined to establish these links. The theory of belief functions is a powerful mathematical tool for combining such uncertain information. In this paper, we introduce a decision pro-cess based on a distance measure to identify the best possible matching entities for a given source entity.

Mouloud Kharoune, Arnaud Martin

Many information sources are considered into data fusion in order to improve the decision in terms of uncertainty and imprecision. For each technique used for data fusion, the asumption on independance is usually made. We propose in this article an approach to take into acount an independance measure befor to make the combination of information in the context of the theory of belief functions.

Jungyeul Park, Mouna Chebbah, Siwar Jendoubi et al.

Hidden Markov Models (HMMs) are learning methods for pattern recognition. The probabilistic HMMs have been one of the most used techniques based on the Bayesian model. First-order probabilistic HMMs were adapted to the theory of belief functions such that Bayesian probabilities were replaced with mass functions. In this paper, we present a second-order Hidden Markov Model using belief functions. Previous works in belief HMMs have been focused on the first-order HMMs. We extend them to the second-order model.

Anthony Fiche, Jean-Christophe Cexus, Arnaud Martin et al.

The aim of this paper is to show the interest in fitting features with an $α$-stable distribution to classify imperfect data. The supervised pattern recognition is thus based on the theory of continuous belief functions, which is a way to consider imprecision and uncertainty of data. The distributions of features are supposed to be unimodal and estimated by a single Gaussian and $α$-stable model. Experimental results are first obtained from synthetic data by combining two features of one dimension and by considering a vector of two features. Mass functions are calculated from plausibility functions by using the generalized Bayes theorem. The same study is applied to the automatic classification of three types of sea floor (rock, silt and sand) with features acquired by a mono-beam echo-sounder. We evaluate the quality of the $α$-stable model and the Gaussian model by analyzing qualitative results, using a Kolmogorov-Smirnov test (K-S test), and quantitative results with classification rates. The performances of the belief classifier are compared with a Bayesian approach.

Siwar Jendoubi, Boutheina Ben Yaghlane, Arnaud Martin

Speech Recognition searches to predict the spoken words automatically. These systems are known to be very expensive because of using several pre-recorded hours of speech. Hence, building a model that minimizes the cost of the recognizer will be very interesting. In this paper, we present a new approach for recognizing speech based on belief HMMs instead of proba-bilistic HMMs. Experiments shows that our belief recognizer is insensitive to the lack of the data and it can be trained using only one exemplary of each acoustic unit and it gives a good recognition rates. Consequently, using the belief HMM recognizer can greatly minimize the cost of these systems.

Siwar Jendoubi, Arnaud Martin, Ludovic Liétard et al.

Nowadays, social networks such as Twitter, Facebook and LinkedIn become increasingly popular. In fact, they introduced new habits, new ways of communication and they collect every day several information that have different sources. Most existing research works fo-cus on the analysis of homogeneous social networks, i.e. we have a single type of node and link in the network. However, in the real world, social networks offer several types of nodes and links. Hence, with a view to preserve as much information as possible, it is important to consider so-cial networks as heterogeneous and uncertain. The goal of our paper is to classify the social message based on its spreading in the network and the theory of belief functions. The proposed classifier interprets the spread of messages on the network, crossed paths and types of links. We tested our classifier on a real word network that we collected from Twitter, and our experiments show the performance of our belief classifier.

Imen Ouled Dlala, Dorra Attiaoui, Arnaud Martin et al.

The web plays an important role in people's social lives since the emergence of Web 2.0. It facilitates the interaction between users, gives them the possibility to freely interact, share and collaborate through social networks, online communities forums, blogs, wikis and other online collaborative media. However, an other side of the web is negatively taken such as posting inflammatory messages. Thus, when dealing with the online communities forums, the managers seek to always enhance the performance of such platforms. In fact, to keep the serenity and prohibit the disturbance of the normal atmosphere, managers always try to novice users against these malicious persons by posting such message (DO NOT FEED TROLLS). But, this kind of warning is not enough to reduce this phenomenon. In this context we propose a new approach for detecting malicious people also called 'Trolls' in order to allow community managers to take their ability to post online. To be more realistic, our proposal is defined within an uncertain framework. Based on the assumption consisting on the trolls' integration in the successful discussion threads, we try to detect the presence of such malicious users. Indeed, this method is based on a conflict measure of the belief function theory applied between the different messages of the thread. In order to show the feasibility and the result of our approach, we test it in different simulated data.

Salma Ben Dhaou, Mouloud Kharoune, Arnaud Martin et al.

Nowadays, social networks became essential in information exchange between individuals. Indeed, as users of these networks, we can send messages to other people according to the links connecting us. Moreover, given the large volume of exchanged messages, detecting the true nature of the received message becomes a challenge. For this purpose, it is interesting to consider this new tendency with reasoning under uncertainty by using the theory of belief functions. In this paper, we tried to model a social network as being a network of fusion of information and determine the true nature of the received message in a well-defined node by proposing a new model: the belief social network.

Jean-Christophe Dubois, Yolande Le Gall, Arnaud Martin

The purpose of this study is to provide an accessibility measure of web-pages, in order to draw disabled users to the pages that have been designed to be ac-cessible to them. Our approach is based on the theory of belief functions, using data which are supplied by reports produced by automatic web content assessors that test the validity of criteria defined by the WCAG 2.0 guidelines proposed by the World Wide Web Consortium (W3C) organization. These tools detect errors with gradual degrees of certainty and their results do not always converge. For these reasons, to fuse information coming from the reports, we choose to use an information fusion framework which can take into account the uncertainty and imprecision of infor-mation as well as divergences between sources. Our accessibility indicator covers four categories of deficiencies. To validate the theoretical approach in this context, we propose an evaluation completed on a corpus of 100 most visited French news websites, and 2 evaluation tools. The results obtained illustrate the interest of our accessibility indicator.

Mouna Chebbah, Mouloud Kharoune, Arnaud Martin et al.

In this paper, we propose to learn sources independence in order to choose the appropriate type of combination rules when aggregating their beliefs. Some combination rules are used with the assumption of their sources independence whereas others combine beliefs of dependent sources. Therefore, the choice of the combination rule depends on the independence of sources involved in the combination. In this paper, we propose also a measure of independence, positive and negative dependence to integrate in mass functions before the combinaision with the independence assumption.

Wiem Maalel, Kuang Zhou, Arnaud Martin et al.

In the data mining field many clustering methods have been proposed, yet standard versions do not take into account uncertain databases. This paper deals with a new approach to cluster uncertain data by using a hierarchical clustering defined within the belief function framework. The main objective of the belief hierarchical clustering is to allow an object to belong to one or several clusters. To each belonging, a degree of belief is associated, and clusters are combined based on the pignistic properties. Experiments with real uncertain data show that our proposed method can be considered as a propitious tool.

Kuang Zhou, Arnaud Martin, Quan Pan et al.

Median clustering is of great value for partitioning relational data. In this paper, a new prototype-based clustering method, called Median Evidential C-Means (MECM), which is an extension of median c-means and median fuzzy c-means on the theoretical framework of belief functions is proposed. The median variant relaxes the restriction of a metric space embedding for the objects but constrains the prototypes to be in the original data set. Due to these properties, MECM could be applied to graph clustering problems. A community detection scheme for social networks based on MECM is investigated and the obtained credal partitions of graphs, which are more refined than crisp and fuzzy ones, enable us to have a better understanding of the graph structures. An initial prototype-selection scheme based on evidential semi-centrality is presented to avoid local premature convergence and an evidential modularity function is defined to choose the optimal number of communities. Finally, experiments in synthetic and real data sets illustrate the performance of MECM and show its difference to other methods.

Kuang Zhou, Arnaud Martin, Quan Pan

Evidential-EM (E2M) algorithm is an effective approach for computing maximum likelihood estimations under finite mixture models, especially when there is uncertain information about data. In this paper we present an extension of the E2M method in a particular case of incom-plete data, where the loss of information is due to both mixture models and censored observations. The prior uncertain information is expressed by belief functions, while the pseudo-likelihood function is derived based on imprecise observations and prior knowledge. Then E2M method is evoked to maximize the generalized likelihood function to obtain the optimal estimation of parameters. Numerical examples show that the proposed method could effectively integrate the uncertain prior infor-mation with the current imprecise knowledge conveyed by the observed data.