针对有向图的局部扩展的重叠社区发现算法

当前社区发现算法主要是针对无向图研究社区结构,但在实际复杂网络中,链接关系时常表现出非对称性或方向性,比如Twitter的用户关注关系,文献网络的引 用关系,网页之间的超链接关系等应用网络。因此,本文依据信息在复杂网络中的传播规律和流动方向性,提出了k-Path共社区邻近相似性概念及计算方法,用于衡量结点在同一社区的相似性程度,并给出了把有向图转换为带方向权值的无向图的方法。基于带权无向图提出了一种从局部扩展来探测社区的重叠社区发现算法(Local and wave-like extension algorithm of detecting overlapping community, LWS-OCD)。在真实数据集上的实验表明,共社区邻近相似性概念实现了有向到无向的合理转换,而且提高了社区结点的聚集效果,LWS-OCD算法能够有效地发现带权无向图中的重叠社区。     

Subgraph similarity maximal all-matching over a large uncertain graph

Recently, uncertain graph data management and mining techniques have attracted significant interests and research efforts due to potential applications such as protein interaction networks and social networks. Specifically, as a fundamental problem, subgraph similarity all-matching is widely applied in exploratory data analysis. The purpose of subgraph similarity all-matching is to find all the similarity occurrences of the query graph in a large data graph. Numerous algorithms and pruning methods have been developed for the subgraph matching problem over a certain graph. However, insufficient efforts are devoted to subgraph similarity all-matching over an uncertain data graph, which is quite challenging due to high computation costs. In this paper, we define the problem of subgraph similarity maximal all-matching over a large uncertain data graph and propose a framework to solve this problem. To further improve the efficiency, several speed-up techniques are proposed such as the partial graph evaluation, the vertex pruning, the calculation model transformation, the incremental evaluation method and the probability upper bound filtering. Finally, comprehensive experiments are conducted on real graph data to test the performance of our framework and optimization methods. The results verify that our solutions can outperform the basic approach by orders of magnitudes in efficiency.     

基于复杂网络的社区发现算法研究

近年来,高质量社区的挖掘和发现已经成为复杂网络研究的一个热点。目前大多的社区发现算法主要针对无向网络,但现在的很多真实网络通常都是有向加权的。同时,标签传播算法(LPA)是一种接近线性复杂度的社区发现算法,该算法具有简单高效、不需要提供社区规模和社区个数等先验知识的特点,因而得到了广泛关注和应用。针对有向加权网络,提出了一种基于节点重要性和节点相似性的改进标签传播算法(CRJ-LPA)。该算法综合考虑节点的边权、节点的信息传播能力、节点相似度以及节点集聚系数等因素。算法通过加权的ClusterRank获得节点重要性列表用以避免LPA中的随机选择;然后,采用Jaccard系数度量节点的相似度,结合节点重要性列表计算出一个新的度量CRJ(重要度和相似度),提高了算法的稳定性。实验结果表明,该算法有效可行,且具有较好的鲁棒性。     

基于路径映射的相似子图匹配算法

迄今为止,相关的图相似性匹配方法通常不考虑节点关系以及边权重的实际意义。提出一种基于路径映射 的相似子图匹配方法,用以更精确地查找具有相似拓扑结构的加权图。其创新之处在于充分利用标签信息,综合考虑 拓扑结构特征,克服了忽略节点结构关系和边权重的意义去分析图相似性的弊端。因此,该方法在很大程度上提高了 图相似性匹配的应用范围和匹配精度。实验表明本方法具有较高的查询质量和效率。     

结构-属性平衡图节点相似度测量算法

摘  要：节点相似度是图聚类算法的重要基础,在基于结构-属性图聚类现有方法中,由于传统图模型的限制,需要多次矩阵相乘来调整属性边的权值,算法执行效率低。为解决这一问题,提出了结构-属性平衡图的概念,并采用随机游走模型策略统一度量结构-属性平衡图GB中顶点间的相似度。与现有方法相比,该方法不但能测量直接相连的顶点之间的相似度,还可测量不直接相连而存在不同长度的路径的顶点之间的相似度,且没有增加原相似度矩阵的规模,节省了大量存储空间,提高了算法执行效率。     

Complete Mining of Frequent Patterns from Graphs: Mining Graph Data

Basket Analysis, which is a standard method for data mining, derives frequent itemsets from database. However, its mining ability is limited to transaction data consisting of items. In reality, there are many applications where data are described in a more structural way, e.g. chemical compounds and Web browsing history. There are a few approaches that can discover characteristic patterns from graph-structured data in the field of machine learning. However, almost all of them are not suitable for such applications that require a complete search for all frequent subgraph patterns in the data. In this paper, we propose a novel principle and its algorithm that derive the characteristic patterns which frequently appear in graph-structured data. Our algorithm can derive all frequent induced subgraphs from both directed and undirected graph structured data having loops (including self-loops) with labeled or unlabeled nodes and links. Its performance is evaluated through the applications to Web browsing pattern analysis and chemical carcinogenesis analysis.     

基于仿射传播的有向网络聚类算法

现有大多数的网络聚类方法都只是针对无向网络, 已有的有向网络聚类方法建立在传统聚类算法基础之上, 存在着一定的局限性。针对上述问题, 提出一种基于仿射传播的有向网络聚类算法, 该算法首先采用SimRank作为节点之间的相似度, 并将计算得到的结果转换为适应于仿射传播算法的负值; 然后将相似度矩阵作为输入, 利用具有更好性能的仿射传播算法对有向网络进行聚类。实验结果表明, 所提出算法的聚类性能优于其他几种具有代表性的有向网络聚类算法。     

基于三元组结构的有向网链路预测方法

当前链路预测的研究主要集中在无向网络,然而现实世界中存在大量的有向网络,忽略链路的方向会缺失一些重要信息甚至使预测失去意义,而直接将无向网络的预测方法应用于有向网络又存在预测精度降低的问题。为此,提出了一个基于三元组的有向网络链路预测算法,该算法针对有向网络和无向网络三元组结构的不同,应用势理论对三元组进行筛选,通过统计分析不同三元组闭合的可能性,以网络整体三元组闭合指数作为权重计算节点间的相似性。在9个真实数据集上的实验表明,所提方法比基准方法的预测精度提高了4.3%。     

基于邻居信息聚合的子图同构匹配算法

图匹配在现实中被广泛运用,而子图同构匹配是其中的研究热点,具有重要的科学意义与实践价值。现有子图同构匹配算法大多基于邻居关系来构建约束条件,而忽略了节点的局部邻域信息。对此,提出了一种基于邻居信息聚合的子图同构匹配算法。首先,将图的属性和结构导入到改进的图卷积神经网络中进行特征向量的表示学习,从而得到聚合后的节点局部邻域信息;然后,根据图的标签、度等特征对匹配顺序进行优化,以提高算法的效率;最后,将得到的特征向量和优化的匹配顺序与搜索算法相结合,建立子图同构的约束满足问题（CSP）模型,并结合CSP回溯算法对模型进行求解。实验结果表明,与经典的树搜索算法和约束求解算法相比,该算法可以有效地提高子图同构的求解效率。     

Approximating Node Connectivity Problems via Set Covers

Given a graph (directed or undirected) with costs on the edges, and an integer $k$, we consider the problem of finding a $k$-node connected spanning subgraph of minimum cost. For the general instance of the problem (directed or undirected), there is a simple $2k$-approximation algorithm. Better algorithms are known for various ranges of $n,k$. For undirected graphs with metric costs Khuller and Raghavachari gave a $( 2+{2(k-1)}/{n})$-approximation algorithm. We obtain the following results: (i) For arbitrary costs, a $k$-approximation algorithm for undirected graphs and a $(k+1)$-approximation algorithm for directed graphs. (ii) For metric costs, a $(2+({k-1})/{n})$-approximation algorithm for undirected graphs and a $(2+{k}/{n})$-approximation algorithm for directed graphs. For undirected graphs and $k=6,7$, we further improve the approximation ratio from $k$ to $\lceil (k+1)/2 \rceil=4$; previously, $\lceil (k+1)/2 \rceil$-approximation algorithms were known only for $k \leq 5$. We also give a fast $3$-approximation algorithm for $k=4$. The multiroot problem generalizes the min-cost $k$-connected subgraph problem. In the multiroot problem, requirements $k_u$ for every node $u$ are given, and the aim is to find a minimum-cost subgraph that contains $\max\{k_u,k_v\}$ internally disjoint paths between every pair of nodes $u,v$. For the general instance of the problem, the best known algorithm has approximation ratio $2k$, where $k=\max k_u$. For metric costs there is a 3-approximation algorithm. We consider the case of metric costs, and, using our techniques, improve for $k \leq 7$ the approximation guarantee from $3$ to $2+{\lfloor (k-1)/2 \rfloor}/{k} < 2.5$.     

LSI芯片图象的双子图同构匹配法

本文提出一种用于LSI芯片图象的双子图同构匹配方法.该方法是在芯片分割图象的区 域邻接图上搜索同构匹配结点间的对应关系. 同构匹配算法利用启发信息提高搜索的效率.算法根据专门建立的区域相似性度量和环 境串匹配值这些判据选取同构匹配起始结点. 文中将详细说明双子图同构匹配法的原理,并提供匹配结果.本算法已在实际中采用.     

Adding regular expressions to graph reachability and pattern queries

It is increasingly common to find graphs in which edges are of different types, indicating a variety of relationships. For such graphs we propose a class of reachability queries and a class of graph patterns, in which an edge is specified with a regular expression of a certain form, expressing the connectivity of a data graph via edges of various types. In addition, we define graph pattern matching based on a revised notion of graph simulation. On graphs in emerging applications such as social networks, we show that these queries are capable of finding more sensible information than their traditional counterparts. Better still, their increased expressive power does not come with extra complexity. Indeed, (1) we investigate their containment and minimization problems, and show that these fundamental problems are in quadratic time for reachability queries and are in cubic time for pattern queries. (2) We develop an algorithm for answering reachability queries, in quadratic time as for their traditional counterpart. (3) We provide two cubic-time algorithms for evaluating graph pattern queries, as opposed to the NP-completeness of graph pattern matching via subgraph isomorphism. (4) The effectiveness and efficiency of these algorithms are experimentally verified using real-life data and synthetic data.     

节点层次化的二进制文件比对技术

当前二进制文件比对技术主流是以BinDiff为代表的结构化比对方法,存在结构相似导致的误匹配、分析耗时较高的问题。针对该问题提出一种基于节点层次化、价值化的匹配方法。通过提取函数节点在函数调用图中的层次与函数在调用网络中的价值,对层次模糊的节点提供了节点层次估算算法,最后递归匹配节点。实验表明,该方法避免了结构相似导致的误匹配,其时耗低于结构化比对工具Bindiff的1/2,节点匹配数量减少在15%以内。该方法可有效提高嵌入式设备固件的跨版本相似性分析效率。     

A conditional independence algorithm for learning undirected graphical models

When it comes to learning graphical models from data, approaches based on conditional independence tests are among the most popular methods. Since Bayesian networks dominate research in this field, these methods usually refer to directed graphs, and thus have to determine not only the set of edges, but also their direction. At least for a certain kind of possibilistic graphical models, however, undirected graphs are a much more natural basis. Hence, in this area, algorithms for learning undirected graphs are desirable, especially, since first learning a directed graph and then transforming it into an undirected one wastes resources and computation time. In this paper I present a general algorithm for learning undirected graphical models, which is strongly inspired by the well-known Cheng–Bell–Liu algorithm for learning Bayesian networks from data. Its main advantage is that it needs fewer conditional independence tests, while it achieves results of comparable quality.     

融合启发式和Boosting的子图匹配基数估计方法

由于在建模关联信息方面具备天然优势,图数据已在社交网络、知识表示等方面被广泛运用.但是相较于传统的关系型数据库系统,图数据管理中的以子图匹配为代表的一系列基础操作仍有进一步优化的空间.在一个完善的图数据库系统中,为实现多个子图匹配任务的优化调度,往往需要对每个任务的代价,尤其是匹配结果的基数进行准确预估.然而,现有的子...     

多编码树GPU并行轴心子图匹配

子图同构问题是非确定多项式(NP)完全问题,而轴心子图同构是一种特殊的子图同构问题.针对现在已经有许多高效的子图同构算法,然而对于轴心子图同构问题目前并没有基于GPU的搜索算法,且通过改造已有的子图同构算法来解决轴心子图匹配问题会产生大量不必要的中间结果这一问题,提出了一种基于GPU的轴心子图同构算法.首先,通过一种新...     

图模型匹配:一种新的凹松弛函数及算法

将问题中的置换矩阵放松为双随机矩阵是近年来近似图匹配算法的一个重要发展方向. 它的本质在于将离散的图匹配问题转换成一个连续优化问题,而一般来讲, 相对于离散优化,连续优化问题的近似求解将更为容易. 但随之带来的一个问题是如何有效地将连续优化得到的双随机矩阵重新映射回一个置换矩阵. 最近文献中提出了一种针对于无向无自环图的凹松弛(Concave relaxation)函数,使得算法中的双随机矩阵可以平滑地收敛到一个置换矩阵, 并得到优异的匹配精度.但除了无向且无自环图,文献中还没有针对其他类型图模型的凹松弛函数. 本文提出一种针对于有向无自环图匹配问题的凹松弛函数, 并在此基础上给出一种图匹配算法.大量对比实验验证了本文提出模型及算法的有效性.     

Matching graphs with unique node labels

A special class of graphs is introduced in this paper. The graphs belonging to this class are characterised by the existence of unique node labels. A number of matching algorithms for graphs with unique node labels are developed. It is shown that problems such as graph isomorphism, subgraph isomorphism, maximum common subgraph (MCS) and graph edit distance (GED) have a computational complexity that is only quadratic in the number of nodes. Moreover, computing the median of a set of graphs is only linear in the cardinality of the set. In a series of experiments, it is demonstrated that the proposed algorithms run very fast in practice. The considered class makes the matching of large graphs, consisting of thousands of nodes, computationally tractable. We also discuss an application of the considered class of graphs and related matching algorithms to the classification and detection of abnormal events in computer networks.     

一种基于相似性聚类的社会网络合作模式发现方法

社会网络上的模式挖掘是近年来的研究热点之一,合作模式是社会网络上个体间的合作方式,这种模式可以通过社会网络的子结构表示。已有的基于频繁模式的挖掘算法主要考虑合作关系的结构特征,并且往往需要给定支持度阈值来控制结果的规模。在本文中,我们认为社会网络中的模式不一定需要是频繁的,模式与社区也并不需要精确匹配。我们在合作模式中考虑节点的社会地位,并在加权图上给出了一种模式的定义方法,和一种基于互相似性的模式匹配衡量标准,目的在于找出网络中具有"代表性"的合作模式。我们设计了一种基于距离的聚类方法用于抽取这种模式,并在一个大规模的真实数据集上进行了验证。     

节点不对称转移概率的网络社区发现算法

社区发现是当前社会网络研究领域的一个热点和难点,现有的研究方法包括：（1）优化以网络拓扑结构为基础的社区质量指标;（2）评估节点间的相似性并进行聚类;（3）根据特定网络设计相应的社区模型等.这些方法存在如下问题：（1）通用性不高,难以同时在无向网络和有向网络上发挥出好的效果;（2）无法充分利用网络的结构信息,在真实数据集上表现不佳.针对上述问题,提出一种基于节点不对称转移概率的网络社区发现算法CDATP.该算法通过分析网络拓扑结构来设计节点转移概率,并使用random walk方法评估节点对网络社区的重要性.最后,以重要性较高的节点作为核心构造网络社区.与现有的基于random walk的方法不同,CDATP为网络中节点设计的转移概率具有不对称性,并只通过节点局部转移来评估节点对社区的重要程度.通过大量仿真实验表明,CDATP在人工模拟数据集和真实数据集上均比其他最新算法有更好的表现.