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Estimation in a binomial stochastic blockmodel for a weighted graph by a variational expectation maximization algorithm
Communications in Statistics - Simulation and Computation ( IF 0.9 ) Pub Date : 2020-05-07 , DOI: 10.1080/03610918.2020.1743858
Abir El Haj 1, 2 , Yousri Slaoui 1 , Pierre-Yves Louis 1 , Zaher Khraibani 2
Affiliation  

Abstract

Stochastic blockmodels have been widely proposed as a probabilistic random graph model for the analysis of networks data as well as for detecting community structure in these networks. In a number of real-world networks, not all ties among nodes have the same weight. Ties among networks nodes are often associated with weights that differentiate them in terms of their strength, intensity, or capacity. In this paper, we are interested in the case of co-citation networks, where the nodes are words and each edge joining a pair of words is weighted by the number of co-citation of these two words together in the same document. In this type of networks, the weight associated to each edge is an integer value bounded by the the whole number of documents in the considered corpus. Hence, we propose an extension of the stochastic blockmodels to deal with the case of a binomial distribution for the edge’s weights. We provide an inference method through a variational expectation maximization algorithm to estimate the parameters in binomial stochastic blockmodels for weighted networks. To prove the validity of the method and to highlight its main features, we set some applications of the proposed approach by using some simulated data and then some real data sets. Stochastic blockmodels belong to latent classes models. Classes defines a node’s clustering. We compare the clustering found through binomial stochastic blockmodels with the ones found fitting a stochastic blockmodel with Poisson distributed edges’ weights. Inferred Poisson and binomial stochastic blockmodels mainly differs. Moreover, in our examples, the statistical error is lower for binomial stochastic blockmodels.



中文翻译:

通过变分期望最大化算法估计加权图的二项式随机块模型

摘要

随机块模型已被广泛提出作为一种概率随机图模型,用于分析网络数据以及检测这些网络中的社区结构。在许多现实世界的网络中,并非所有节点之间的关系都具有相同的权重。网络节点之间的联系通常与在强度、强度或容量方面区分它们的权重相关联。在本文中,我们对共引网络感兴趣,其中节点是单词,连接一对单词的每条边由这两个单词在同一文档中的共引次数加权。在这种类型的网络中,与每条边相关的权重是一个整数值,以所考虑的语料库中的文档总数为界。因此,我们提出了随机块模型的扩展,以处理边缘权重的二项式分布的情况。我们通过变分期望最大化算法提供了一种推理方法来估计加权网络的二项式随机块模型中的参数。为了证明该方法的有效性并突出其主要特征,我们通过使用一些模拟数据和一些真实数据集来设置该方法的一些应用。随机块模型属于潜在类模型。类定义节点的集群。我们将通过二项式随机块模型发现的聚类与发现拟合具有泊松分布边权重的随机块模型的聚类进行比较。推断泊松和二项式随机块模型主要不同。此外,在我们的示例中,

更新日期:2020-05-07
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