Kuang Zhou

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.

ECMdd: Evidential c-medoids clustering with multiple prototypes

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.

A similarity-based community detection method with multiple prototype representation

Communities are of great importance for understanding graph structures in social networks. Some existing community detection algorithms use a single prototype to represent each group. In real applications, this may not adequately model the different types of communities and hence limits the clustering performance on social networks. To address this problem, a Similarity-based Multi-Prototype (SMP) community detection approach is proposed in this paper. In SMP, vertices in each community carry various weights to describe their degree of representativeness. This mechanism enables each community to be represented by more than one node. The centrality of nodes is used to calculate prototype weights, while similarity is utilized to guide us to partitioning the graph. Experimental results on computer generated and real-world networks clearly show that SMP performs well for detecting communities. Moreover, the method could provide richer information for the inner structure of the detected communities with the help of prototype weights compared with the existing community detection models.

Evidential Communities for Complex Networks

Community detection is of great importance for understand-ing graph structure in social networks. The communities in real-world networks are often overlapped, i.e. some nodes may be a member of multiple clusters. How to uncover the overlapping communities/clusters in a complex network is a general problem in data mining of network data sets. In this paper, a novel algorithm to identify overlapping communi-ties in complex networks by a combination of an evidential modularity function, a spectral mapping method and evidential c-means clustering is devised. Experimental results indicate that this detection approach can take advantage of the theory of belief functions, and preforms good both at detecting community structure and determining the appropri-ate number of clusters. Moreover, the credal partition obtained by the proposed method could give us a deeper insight into the graph structure.

Evidential-EM Algorithm Applied to Progressively Censored Observations

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.

SELP: Semi-supervised evidential label propagation algorithm for graph data clustering

With the increasing size of social networks in the real world, community detection approaches should be fast and accurate. The label propagation algorithm is known to be one of the near-linear solutions which is easy to implement. However, it is not stable and it cannot take advantage of the prior information about the network structure which is very common in real applications. In this paper, a new Semi-supervised clustering approach based on an Evidential Label Propagation strategy (SELP) is proposed to incorporate limited domain knowledge into the community detection model. The main advantage of SELP is that it can effectively use limited supervised information to guide the detection process. The prior information about the labels of nodes in the graph, including the labeled nodes and the unlabeled ones, is initially expressed in the form of mass functions. Then the evidential label propagation rule is designed to propagate the labels from the labeled nodes to the unlabeled ones. The communities of each node can be identified after the propagation process becomes stable. The outliers can be identified to be in a special class. Experimental results demonstrate the effectiveness of SELP on both graphs and classical data sets.

Evidence combination for a large number of sources

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 more reliable 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 functions verify that the rule can be effectively used to combine a large number of mass functions and to elicit the major opinion.

Pattern classification based on the combination of the selected sources of evidence

In the complex pattern classification problem, the fusion of multiple classification results produced by different attributes is able to efficiently improve the accuracy. Evidence theory is good at representing and combining the uncertain information, and it is employed here. Each attribute (set) can be considered as one source of evidence (information). In some applications, the observation of target attributes can be costly, and some unreliable information sources may harm the fusion result. Therefore, we want to use as few as possible sources of information with high quality to achieve the admissible classification accuracy. So we propose a new fusion method based on the adaptive selection of the information sources for pattern classification. For each pattern, the attribute (set) producing the highest accuracy among the various ones will be chosen to classify the pattern at first. If the reliability of classification result, which is evaluated by the K-nearest neighbors (K-NN) technique using training data, cannot satisfy the request, the next attribute source will be chosen according to its classification performance on the selected neighborhoods of the object. In the fusion, the classification results corresponding to different attributes are assigned different weights because of their different classification abilities, and the weighted evidence combination method is adopted to produce the best possible classification performance. Several real data sets from UCI have been used for the evaluation of the proposed method by comparison with other related fusion methods, and it shows that our new method can produce higher accuracy with smaller number of information sources than the other fusion methods which are directly used to combine all the sources of information.

The advantage of evidential attributes in social networks

Currently, 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 can 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 can detect communities for 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 give better results comparing to those with probabilistic and numerical attributes. This illustrates the advantages of evidential attributes.

Semi-supervised Evidential Label Propagation Algorithm for Graph Data

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.