Evidential Label Propagation Algorithm for Graphs

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.Comment: 19th International Conference on Information Fusion, Jul 2016, Heidelber, Franc

Median evidential c-means algorithm and its application to community detection

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

Adaptive imputation of missing values for incomplete pattern classification

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

Evidential relational clustering using medoids

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.Comment: in The 18th International Conference on Information Fusion, July 2015, Washington, DC, USA , Jul 2015, Washington, United State

EGMM: an Evidential Version of the Gaussian Mixture Model for Clustering

The Gaussian mixture model (GMM) provides a convenient yet principled framework for clustering, with properties suitable for statistical inference. In this paper, we propose a new model-based clustering algorithm, called EGMM (evidential GMM), in the theoretical framework of belief functions to better characterize cluster-membership uncertainty. With a mass function representing the cluster membership of each object, the evidential Gaussian mixture distribution composed of the components over the powerset of the desired clusters is proposed to model the entire dataset. The parameters in EGMM are estimated by a specially designed Expectation-Maximization (EM) algorithm. A validity index allowing automatic determination of the proper number of clusters is also provided. The proposed EGMM is as convenient as the classical GMM, but can generate a more informative evidential partition for the considered dataset. Experiments with synthetic and real datasets demonstrate the good performance of the proposed method as compared with some other prototype-based and model-based clustering techniques

Evidence combination based on credal belief redistribution for pattern classification

Evidence theory, also called belief functions theory, provides an efficient tool to represent and combine uncertain information for pattern classification. Evidence combination can be interpreted, in some applications, as classifier fusion. The sources of evidence corresponding to multiple classifiers usually exhibit different classification qualities, and they are often discounted using different weights before combination. In order to achieve the best possible fusion performance, a new Credal Belief Redistribution (CBR) method is proposed to revise such evidence. The rationale of CBR consists in transferring belief from one class not just to other classes but also to the associated disjunctions of classes (i.e., meta-classes). As classification accuracy for different objects in a given classifier can also vary, the evidence is revised according to prior knowledge mined from its training neighbors. If the selected neighbors are relatively close to the evidence, a large amount of belief will be discounted for redistribution. Otherwise, only a small fraction of belief will enter the redistribution procedure. An imprecision matrix estimated based on these neighbors is employed to specifically redistribute the discounted beliefs. This matrix expresses the likelihood of misclassification (i.e., the probability of a test pattern belonging to a class different from the one assigned to it by the classifier). In CBR, the discounted beliefs are divided into two parts. One part is transferred between singleton classes, whereas the other is cautiously committed to the associated meta-classes. By doing this, one can efficiently reduce the chance of misclassification by modeling partial imprecision. The multiple revised pieces of evidence are finally combined by Dempster-Shafer rule to reduce uncertainty and further improve classification accuracy. The effectiveness of CBR is extensively validated on several real datasets from the UCI repository, and critically compared with that of other related fusion methods

Evidential relational clustering using medoids

Abstract-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

Evidential relational clustering using medoids

International audienceIn 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

H2S biosynthesis and catabolism: new insights from molecular studies

Hydrogen sulfide (H2S) has profound biological effects within living organisms and is now increasingly being considered alongside other gaseous signalling molecules, such as nitric oxide (NO) and carbon monoxide (CO). Conventional use of pharmacological and molecular approaches has spawned a rapidly growing research field that has identified H2S as playing a functional role in cell-signalling and post-translational modifications. Recently, a number of laboratories have reported the use of siRNA methodologies and genetic mouse models to mimic the loss of function of genes involved in the biosynthesis and degradation of H2S within tissues. Studies utilising these systems are revealing new insights into the biology of H2S within the cardiovascular system, inflammatory disease, and in cell signalling. In light of this work, the current review will describe recent advances in H2S research made possible by the use of molecular approaches and genetic mouse models with perturbed capacities to generate or detoxify physiological levels of H2S gas within tissue

Classification crédibiliste de données incertaines fondée sur la théorie des fonctions de croyances

Modeling and managing uncertainty in the classification problem remains an important and interesting research topic. Credal classification of uncertain data based on belief function theory has been studied in this thesis, and it allows the object to belong not only to the single classes, but also to any set of classes (called meta-class) with different masses of belief. The credal classification is then of interest to explore the imprecision of classes. Classification methods can be mainly identified by supervised, unsupervised and semi-supervised ones according to the availability of training information. We focus on the supervised and unsupervised classifications. When there are a lot of training samples available in the classification, two credal classifiers for uncertain data are proposed for dealing with different cases. A belief c × K neighbors (BCKN) classifier has been proposed based on belief function theory. In BCKN, the query object is classified according to its K nearest neighbors in each class, and c × K basic belief assignments (BBA¿s) are determined according to the distances between the object and these neighbors, and the global fusion of them is used for the credal classification of object. When each class of data can be represented by the prototype vector, a simple credal classification rule (CCR) has been developed using belief functions. Moreover, the missing attribute data is often encountered in classification problem. The different estimations of the missing values can lead to distinct classification results sometimes, and this yields high imprecision and uncertainty of classification due to the lack of information in the missing values.Cette thèse s'intéresse à la classification crédibiliste de données fondée sur la théorie des fonctions de masse. Lorsque des échantillons labellisés sont disponibles en nombre suffisant, une classification supervisée peut être appliquée. Certains classifieurs ont été développés sur la base de la théorie de Demspter-Shafer, et l'ignorance totale est caractérisée en utilisant une pondération des fonctions de masse. Or, l'information imprécise partielle n'est pas prise en compte dans ces méthodes, et la classification est souvent partiellement imprécise entre un très petit nombre de classes. Dans cette thèse, nous avons étudié la classification crédibiliste de données incertaines sur la base des fonctions de croyance, et deux classifieurs crédibilistes ont été proposés. La classification crédibiliste permet à un objet d'appartenir à des classes simples mais aussi à des méta-classes définies par l'union de plusieurs classes simples. Ces méta-classes modélisent l'imprécision partielle de classification et réduisent le taux d'erreur de classification. Une méthode de classification crédibiliste appelée c × K plus proches voisins crédibilistes a été introduite. Lorsque chaque classe peut être représentée par son centre de classe, nous avons également proposé une règle simple de classification crédibiliste (CCR), qui calcule directement la masse de croyance de l'échantillon appartenant à chaque classe et une méta-classe avec une faible complexité calculatoire. En outre, une méthode de classification crédibiliste de données incomplètes a été également développée, et elle est capable de modéliser de telles informations incertaines et imprécises provenant de valeurs manquantes