Structural learning for Bayesian networks by testing complete separators in prime blocks

In this paper, we consider how to recover the structure of a Bayesian network from a moral graph. We present a more accurate characterization of moral edges, based on which a complete subset (i.e., a separator) contained in the neighbor set of one vertex of the putative moral edge in some prime block of the moral graph can be chosen. This results in a set of separators needing to be searched generally smaller than the sets required by some existing algorithms. A so-called structure-finder algorithm is proposed for structural learning. The complexity analysis of the proposed algorithm is discussed and compared with those for several existing algorithms. We also demonstrate how to construct the moral graph locally from, separately, the Markov blanket, domain knowledge and d-separation trees. Simulation studies are used to evaluate the performances of various strategies for structural learning. We also analyze a gene expression data set by using the structure-finder algorithm.     

Periodic subgraph mining in dynamic networks

In systems of interacting entities such as social networks, interactions that occur regularly typically correspond to significant, yet often infrequent and hard to detect, interaction patterns. To identify such regular behavior in streams of dynamic interaction data, we propose a new mining problem of finding a minimal set of periodically recurring subgraphs to capture all periodic behavior in a dynamic network. We analyze the computational complexity of the problem and show that it is polynomial, unlike many related subgraph or itemset mining problems. We propose an efficient and scalable algorithm to mine all periodic subgraphs in a dynamic network. The algorithm makes a single pass over the data and is also capable of accommodating imperfect periodicity. We demonstrate the applicability of our approach on several real-world networks and extract interesting and insightful periodic interaction patterns. We also show that periodic subgraphs can be an effective way to uncover and characterize the natural periodicities in a system.     

基于子图分解的图聚类神经网络

聚类是机器学习的核心任务之一,其主要目的是将无标签数据中的不同簇数据进行分离。深度聚类算法使用深度神经网络联合优化聚类目标与特征提取,极大地提高了聚类性能。图聚类是深度聚类领域近两年研究的一个重要分支,其在处理图结构数据上有极大的优势。提出一种新的图聚类方案：基于子图分解的图聚网络,该模型在图自编码器的基础上通过构建多个子图,并在子图的嵌入空间中加以组稀疏约束达到最终的聚类目的。     

Efficient subgraph isomorphism detection: a decomposition approach

Graphs are a powerful and universal data structure useful in various subfields of science and engineering. In this paper, we propose a new algorithm for subgraph isomorphism detection from a set of a priori known model graphs to an input graph that is given online. The new approach is based on a compact representation of the model graphs that is computed offline. Subgraphs that appear more than once within the same or within different model graphs are represented only once, thus reducing the computational effort to detect them in an input graph. In the extreme case where all model graphs are highly similar, the run-time of the new algorithm becomes independent of the number of model graphs. Both a theoretical complexity analysis and practical experiments characterizing the performance of the new approach are given     

Two-stream adaptive-attentional subgraph convolution networks for skeleton-based action recognition

Multimedia Tools and Applications - Recently, skeleton-based action recognition has modeled the human skeleton as a graph convolution network (GCN), and has achieved remarkable results. However,...     

A prime decomposition theorem for grammatical families

Two basic operations on families of languages, in general, and grammatical families, in particular, are sum (formed by taking unions of member languages) and product (formed by taking unions of pairwise products of member languages). In this paper, a grammatical family is defined to be prime if it is contained in one of two grammatical families whenever it is contained in their product, and the following Prime Decomposition Theorem is then established: Every grammatical family can be represented as a minimal sum of products of primes in a unique way.This theorem leads to a general method for decomposing a grammatical family into simpler ones. A subsequent paper uses this method to obtain a decision procedure for determining whether two grammar forms generate the same grammatical family, as well as a canonical representation for grammatical families.     

基于d-邻域子图匿名的社会网络隐私保护*

社会网络分析可能会侵害到个体的隐私信息,需要在发布的同时进行隐私保护。针对社会网络发布中存在的邻域攻击问题,提出了基于超边矩阵表示的d-邻域子图k-匿名模型。该模型采用矩阵表示顶点的d-邻域子图,通过矩阵的匹配来实现子图的k-匿名,使得匿名化网络中的每个节点都拥有不少于k个同构的d-邻域子图。实验结果表明该模型能够有效地抵制邻域攻击,保护隐私信息。     

Bayesian learning of Bayesian networks with informative priors

This paper presents and evaluates an approach to Bayesian model averaging where the models are Bayesian nets (BNs). A comprehensive study of the literature on structural priors for BNs is conducted. A number of prior distributions are defined using stochastic logic programs and the MCMC Metropolis-Hastings algorithm is used to (approximately) sample from the posterior. We use proposals which are tightly coupled to the priors which give rise to cheaply computable acceptance probabilities. Experiments using data generated from known BNs have been conducted to evaluate the method. The experiments used 6 different BNs and varied: the structural prior, the parameter prior, the Metropolis-Hasting proposal and the data size. Each experiment was repeated three times with different random seeds to test the robustness of the MCMC-produced results. Our results show that with effective priors (i) robust results are produced and (ii) informative priors improve results significantly.     

Evaluation of subgraph searching algorithms detecting network motif in biological networks

Despite several algorithms for searching subgraphs in motif detection presented in the literature, no effort has been done for characterizing their performance till now. This paper presents a methodology to evaluate the performance of three algorithms: edge sampling algorithm (ESA), enumerate subgraphs (ESU) and randomly enumerate subgraphs (RAND-ESU). A series of experiments are performed to test sampling speed and sampling quality. The results show that RAND-ESU is more efficient and has less computational cost than other algorithms for large-size motif detection, and ESU has its own advantage in small-size motif detection.     

Restricted Bayesian classification networks

Bayesian networks are graphical models that describe dependency relationships between variables, and are powerful tools for studying probability classifiers. At present, the causal Bayesian network learning method is used in constructing Bayesian network classifiers while the contribution of attribute to class is over-looked. In this paper, a Bayesian network specifically for classification-restricted Bayesian classification networks is proposed. Combining dependency analysis between variables, classification accuracy evaluation criteria and a search algorithm, a learning method for restricted Bayesian classification networks is presented. Experiments and analysis are done using data sets from UCI machine learning repository. The results show that the restricted Bayesian classification network is more accurate than other well-known classifiers.     

Evaluation of subgraph searching algorithms for detecting network motifs in biological networks

Despite several algorithms for searching subgraphs in motif detection presented in the literature, no effort has been done for characterizing their performance till now. This paper presents a methodology to evaluate the performance of three algorithms: edge sampling algorithm (ESA), enumerate subgraphs (ESU) and randomly enumerate subgraphs (RAND-ESU). A series of experiments are performed to test sampling speed and sampling quality. The results show that RAND-ESU is more efficient and has less computational cost than other algorithms for large-size motif detection, and ESU has its own advantage in small-size motif detection.     

Algebraic geometry of Bayesian networks

We study the algebraic varieties defined by the conditional independence statements of Bayesian networks. A complete algebraic classification is given for Bayesian networks on at most five random variables. Hidden variables are related to the geometry of higher secant varieties.     

贝叶斯网络扩展研究综述

贝叶斯网络是一种能够对复杂不确定系统进行推理和建模的有效工具,广泛用于不确定决策、数据分析以及智能推理等领域.由于理论和实际的需要,贝叶斯网络不断扩展,出现了各种模型和研究方法.为此,综述了贝叶斯网络在不同领域的扩展模型以及在不同理论框架下的进展,并展望了未来的几个发展方向.     

Suboptimal network coding subgraph algorithms for 5G minimum-cost multicast networks

To reduce the transmission cost in 5G multicast networks that have separate control and data planes, we focus on the minimum-power-cost network-coding subgraph problem for the coexistence of two multicasts in wireless networks. We propose two suboptimal algorithms as extensions of the Steiner tree multicast. The critical 1-cut path eliminating (C1CPE) algorithm attempts to find the minimum-cost solution for the coexistence of two multicast trees with the same throughput by reusing the links in the topology, and keeps the solution decodable by a coloring process. For the special case in which the two multicast trees share the same source and destinations, we propose the extended selective closest terminal first (E-SCTF) algorithm out of the C1CPE algorithm. Theoretically the complexity of the E-SCTF algorithm is lower than that of the C1CPE algorithm. Simulation results show that both algorithms have superior performance in terms of power cost and that the advantage is more evident in networks with ultra-densification.     

Image interpretation using Bayesian networks

The problem of image interpretation is one of inference with the help of domain knowledge. In this paper, we formulate the problem as the maximum a posteriori (MAP) estimate of a properly defined probability distribution function (PDF). We show that a Bayesian network can be used to represent this PDF as well as the domain knowledge needed for interpretation. The Bayesian network may be relaxed to obtain the set of optimum interpretations