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

k-EVCLUS: Clustering Large Dissimilarity Data in the Belief Function Framework

International audienceIn evidential clustering, the membership of objects to clusters is considered to be uncertain and is represented by mass functions, forming a credal partition. The EVCLUS algorithm constructs a credal partition in such a way that larger dissimilarities between objects correspond to higher degrees of conflict between the associated mass functions. In this paper, we propose to replace the gradient-based optimization procedure in the original EVCLUS algorithm by a much faster iterative row-wise quadratic programming method. We also show that EVCLUS can be provided with only a random sample of the dissimilarities, reducing the time and space complexity from quadratic to linear. These improvements make EVCLUS suitable to cluster large dissimilarity datasets

Evidential Clustering: A Review

International audienceIn evidential clustering, uncertainty about the assignment of objects to clusters is represented by Dempster-Shafer mass functions. The resulting clustering structure, called a credal partition, is shown to be more general than hard, fuzzy, possibilistic and rough partitions, which are recovered as special cases. Three algorithms to generate a credal partition are reviewed. Each of these algorithms is shown to implement a decision-directed clustering strategy. Their relative merits are discussed

A reliability-based approach for influence maximization using the evidence theory

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.Comment: 14 pages, 8 figures, DaWak 2017 conferenc

Combining clusterings in the belief function framework

International audienceIn this paper, we propose a clustering ensemble method based on Dempster-Shafer Theory. In the first step, base partitions are generated by evidential clustering algorithms such as the evidential c-means or EVCLUS. Base credal partitions are then converted to their relational representations, which are combined by averaging. The combined relational representation is then made transitive using the theory of intuitionistic fuzzy relations. Finally, the consensus solution is obtained by minimizing an error function. Experiments with simulated and real datasets show the good performances of this method

A distance measure of interval-valued belief structures

Interval-valued belief structures are generalized from belief function theory, in terms of basic belief assignments from crisp to interval numbers. The distance measure has long been an essential tool in belief function theory, such as conflict evidence combinations, clustering analysis, belief function and approximation. Researchers have paid much attention and proposed many kinds of distance measures. However, few works have addressed distance measures of interval-valued belief structures up. In this paper, we propose a method to measure the distance of interval belief functions. The method is based on an interval-valued one-dimensional Hausdorff distance and Jaccard similarity coefficient. We show and prove its properties of non-negativity, non-degeneracy, symmetry and triangle inequality. Numerical examples illustrate the validity of the proposed distance

Dealing with non-metric dissimilarities in fuzzy central clustering algorithms

Clustering is the problem of grouping objects on the basis of a similarity measure among them. Relational clustering methods can be employed when a feature-based representation of the objects is not available, and their description is given in terms of pairwise (dis)similarities. This paper focuses on the relational duals of fuzzy central clustering algorithms, and their application in situations when patterns are represented by means of non-metric pairwise dissimilarities. Symmetrization and shift operations have been proposed to transform the dissimilarities among patterns from non-metric to metric. In this paper, we analyze how four popular fuzzy central clustering algorithms are affected by such transformations. The main contributions include the lack of invariance to shift operations, as well as the invariance to symmetrization. Moreover, we highlight the connections between relational duals of central clustering algorithms and central clustering algorithms in kernel-induced spaces. One among the presented algorithms has never been proposed for non-metric relational clustering, and turns out to be very robust to shift operations. (C) 2008 Elsevier Inc. All rights reserved