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Recent studies show that individuals in a social network can be divided into different groups of densely connected communities, and these individuals who bridge different communities, referred to as structural hole spanners, have great potential to acquire resources/information from communities and thus benefit from the access. Structural hole spanners are crucial in many real applications such as community detections, diffusion controls, viral marketing, etc. In spite of their importance, little attention has been paid to them. Particularly, how to accurately characterize the structural hole spanners and how to devise efficient yet scalable algorithms to find them in a large social network are fundamental issues. In this paper, we study the top-$k$ structural hole spanner problem. We first provide a novel model to measure the quality of structural hole spanners through exploiting the structural hole spanner properties. Due to its NP-hardness, we then devise two efficient yet scalable algorithms, by developing innovative filtering techniques that can filter out unlikely solutions as quickly as possible, while the proposed techniques are built up on fast estimations of the upper and lower bounds on the cost of an optimal solution and make use of articulation points in real social networks. We finally conduct extensive experiments to validate the effectiveness of the proposed model, and to evaluate the performance of the proposed algorithms using real world datasets. The experimental results demonstrate that the proposed model can capture the characteristics of structural hole spanners accurately, and the structural hole spanners found by the proposed algorithms are much better than those by existing algorithms in all considered social networks, while the running times of the proposed algorithms are very fast. [ABSTRACT FROM AUTHOR]

The neighborhood counting measure is the number of all common neighborhoods between a pair of data points. It can be used as a similarity measure for different types of data through the notion of neighborhood: multivariate, sequence, and tree data. It has been shown that this measure is closely related to a secondary probability G, which is defined in terms of a primary probability P of interest to a problem. It has also been shown that the G probability can be estimated by aggregating neighborhood counts. The following questions can be asked: What is the relationship between this similarity measure and the primary probability P, especially for the task of classification? How does this similarity measure compare with the euclidean distance, since they are directly comparable? How does the C probability estimation compare with the popular kernel density estimation for the task of classification? These questions are answered in this paper, some theoretically and some experimentally. It is shown that C is a linear function of P and, therefore, a C-based Bayes classifier is equivalent to a P-based Bayes classifier. It is also shown that a weighted k-nearest neighbor classifier equipped with the neighborhood counting measure is, in fact, an approximation of the G-based Bayes classifier. It is further shown that the G probability leads to a probability estimator similar in spirit to the kernel density estimator. New experimental results are presented in this paper, which show that this measure compares favorably with the euclidean distance not only on multivariate data but also on time-series data. New experimental results are also presented regarding probability/density estimation. It was found that the C probability estimation can outperform the kernel density estimation in classification tasks. [ABSTRACT FROM AUTHOR]

In this paper, we examine the problem of count data clustering. We analyze this problem using finite mixtures of distributions. The multinomial distribution and the multinomial Dirichiet distribution (MDD) are widely accepted to model count data. We show that these two distributions cannot be the best choice in all the applications, and we propose another model called the multinomial generalized Dirichlet distribution (MGDD) that is the composition of the generalized Dirichlet distribution and the multinomial, in the same way that the MDD is the composition of the Dirichiet and the multinomial. The estimation of the parameters and the determination of the number of components in our model are based on the deterministic annealing expectation-maximization (DAEM) approach and the minimum description length (MDL) criterion, respectively. We compare our method to standard approaches such as multinomial and multinomial Dirichiet mixtures to show its merits. The comparison involves different applications such as spatial color image databases indexing, handwritten digit recognition, and text document clustering. [ABSTRACT FROM AUTHOR]