基于图谱分解和概率神经网络的图像分类

为了准确地对不同学习样本数的图像进行分类,首先讨论了对属于不同类别的图像序列如何进行正确有监督分类的问题,由于解决这类问题首先要选取适合图像分类的图像特征作为分类的依据,为此先用图像角点来构成Delaunay图,然后将由Delaunay图的谱特征形成的分类特征矢量作为分类的依据;其次,由于分类器的选取也直接影响分类结果,为此采用了学习效率高的概率神经网络分类器来进行分类.经过大量分类实验表明,图谱特征很好地保持了图像的结构特征,是理想的图像分类特征;经过与其他相关分类器的分类比较实验表明,基于概率神经网络的分类器可以准确地进行图像分类;通过不同学习样本数的比较,证实了概率神经网络在进行图像分类时,对于学习样本数并不敏感,并具有一定稳定性.     

基于属性嵌入与图注意力网络的实体对齐算法

实体对齐旨在找到位于不同知识图谱中的等效实体,是实现知识融合的重要步骤.当前主流的方法是基于图神经网络的实体对齐方法,这些方法往往过于依赖图的结构信息,导致在特定图结构上训练得到的模型不能拓展应用于其他图结构中.同时,大多数方法未能充分利用辅助信息,例如属性信息.为此,本文提出了一种基于图注意力网络和属性嵌入的实体对齐方法,该方法使用图注意力网络对不同的知识图谱进行编码,引入注意力机制从实体应用到属性,在对齐阶段将结构嵌入和属性嵌入进行结合实现实体对齐效果的提升.在现实世界的3个真实数据集上对本文模型进行了验证,实验结果表明提出的方法在很大程度上优于基准的实体对齐方法.     

一种多到一子图同构检测方法

提出一种方法来解决从多个小图到一个大图的子图同构检测问题,其中多个小图是预先给定的,而大图是用户在线提交的.首先,基于DFS 编码提出一种小图集合的压缩组织方法;其次,提出一种带有前向剪枝技术的从多个小图到一个大图的子图同构检测算法.另外,给出一种有效的基于数据挖掘的索引技术.分析和实验结果证实,所提出方法的在线计算代价远小于现有方法,在线执行时间比现有方法快约一个数量级,离线构造时间快一个数量级以上.     

一种新的高效图聚集算法

图聚集是将一个大规模的图用简洁的并能有效反映原始图的结构和属性信息的小规模图来表示的技术.图聚集在图数据管理、分析和可视化中发挥着重要作用.图聚集方面现有研究结果还很少,也很不系统.其主要不足之处是:1)算法依赖于具体应用;2)算法仅考虑了图的某方面信息,如结构信息或属性信息;3)算法对用户提供的交互和反馈信息的约束很强.针对现有图聚集算法存在的主要不足,提出一种有向图新型图聚集算法,该算法采用一种新的聚集图质量函数,全面刻画了聚集图多样性、覆盖性、简洁性和实用性.该算法使用LSH(locality sensitive Hashing)技术和基于熵的划分技术,保证了聚集图的质量.在真实数据集上进行了大量的实验,验证了算法的有效性.     

The number of spanning trees in a new lexicographic product of graphs

The problem of counting the number of spanning trees is an old topic in graph theory with important applications to reliable network design. Usually, it is desirable to put forward a formula of the number of spanning trees for various graphs, which is not only interesting in its own right but also in practice. Since some large graphs can be composed of some existing smaller graphs by using the product of graphs, the number of spanning trees of such large graph is also closely related to that of the corresponding smaller ones. In this article, we establish a formula for the number of spanning trees in the lexicographic product of two graphs, in which one graph is an arbitrary graph G and the other is a complete multipartite graph. The results extend some of the previous work, which is closely related to the number of vertices and Lapalacian eigenvalues of smaller graphs only.     

Parallel incremental graph partitioning

Partitioning graphs into equally large groups of nodes while minimizing the number of edges between different groups is an extremely important problem in parallel computing. For instance, efficiently parallelizing several scientific and engineering applications requires the partitioning of data or tasks among processors such that the computational load on each node is roughly the same, while communication is minimized. Obtaining exact solutions is computationally intractable, since graph partitioning is NP-complete. For a large class of irregular and adaptive data parallel applications (such as adaptive graphs), the computational structure changes from one phase to another in an incremental fashion. In incremental graph-partitioning problems the partitioning of the graph needs to be updated as the graph changes over time; a small number of nodes or edges may be added or deleted at any given instant. In this paper, we use a linear programming-based method to solve the incremental graph-partitioning problem. All the steps used by our method are inherently parallel and hence our approach can be easily parallelized. By using an initial solution for the graph partitions derived from recursive spectral bisection-based methods, our methods can achieve repartitioning at considerably lower cost than can be obtained by applying recursive spectral bisection. Further, the quality of the partitioning achieved is comparable to that achieved by applying recursive spectral bisection to the incremental graphs from scratch     

Straight-Line Drawing Algorithms for Hierarchical Graphs and Clustered Graphs

Hierarchical graphs and clustered graphs are useful non-classical graph models for structured relational information. Hierarchical graphs are graphs with layering structures; clustered graphs are graphs with recursive clustering structures. Both have applications in CASE tools, software visualization and VLSI design. Drawing algorithms for hierarchical graphs have been well investigated. However, the problem of planar straight-line representation has not been solved completely. In this paper we answer the question: does every planar hierarchical graph admit a planar straight-line hierarchical drawing? We present an algorithm that constructs such drawings in linear time. Also, we answer a basic question for clustered graphs, that is, does every planar clustered graph admit a planar straight-line drawing with clusters drawn as convex polygons? We provide a method for such drawings based on our algorithm for hierarchical graphs.     

一种不确定图数据库上的相似性连接方法

在确定图上进行的相似性连接已有许多研究成果.然而,在实际应用中会有许多因素使得图结构数据变得不确定.研究了不确定图数据库上的相似性连接问题.采用联合概率分布表示法来描述图中边的不确定性,结合一种新的图的相似性度量方法,给出了不确定图数据库上的相似性连接的形式化定义,并设计了一组过滤策略来减少连接过程中候选图对的数量.大量的实验数据表明,所提出的方法具有较好的可行性和准确性.     

医学图像图深度学习分割算法综述

精准分割医学图像中的器官或病灶,是医学图像智能分析领域的重要难题,其在临床上对于疾病的辅助诊疗有着重要应用价值。在解决医学图像信息表征及对非欧空间生理组织结构准确建模等挑战性问题方面,基于图深度学习的医学图像分割技术取得了重要突破,展现出显著的信息特征提取及表征优势,可获得更为精准的分割结果,已成为该领域新兴研究热点。为更好促进医学图像图深度学习分割算法的研究发展,对该领域的技术进展及应用现状做了系统的梳理总结。介绍了图的定义及图卷积网络的基本结构,详细阐述了谱图卷积和空域图卷积操作。根据GCN结合残差模块、注意力机制模块及学习模块三种技术结构模式,归纳并总结了其在医学图像分割中的研究进展。对图深度学习算法在医学图像分割领域的应用和发展做了概要总结和展望,为该领域的技术发展提供参考和新的研究思路。     

知识图谱的增强CP分解链接预测方法

CP分解作为知识图谱链接预测的方法之一,能够对一些包含常规数据的知识图谱进行链接预测补全。但当知识图谱存在大量稀疏数据及可逆关系时,该方法不能体现两个实体间具有的隐藏联系,无法对此类数据进行处理。为解决上述问题,提出增强CP分解方法,对三元组中前实体和后实体的两个嵌入向量分别进行学习,并在训练过程中使用概率方法生成更高质量的负例三元组,引入ELU损失函数和AMSGrad优化器,有效对可逆关系和稀疏数据进行处理。在通用数据集上的实验结果表明,所提方法可以有效提升链接预测精度,与对比模型相比取得了5%的性能提升,同时应用在汽车维修知识图谱数据集补全中,取得83.2%正确率的实体补全结果。     

Finding Minimum Vertex Covering in Stochastic Graphs: A Learning Automata Approach

Structural and behavioral parameters of many real networks such as social networks are unpredictable, uncertain, and have time-varying parameters, and for these reasons, deterministic graphs for modeling such networks are too restrictive to solve most of the real-network problems. It seems that stochastic graphs, in which weights associated to the vertices are random variables, might be better graph models for real-world networks. Once we use a stochastic graph as the model for a network, every feature of the graph such as path, spanning tree, clique, dominating set, and cover set should be treated as a stochastic feature. For example, choosing a stochastic graph as a graph model of an online social network and defining community structure in terms of clique, the concept of a stochastic clique may be used to study community structures’ properties or define spreading of influence according to the coverage of influential users; the concept of stochastic vertex covering may be used to study spread of influence. In this article, minimum vertex covering in stochastic graphs is first defined, and then four learning, automata-based algorithms are proposed for solving a minimum vertex-covering problem in stochastic graphs where the probability distribution functions of the weights associated with the vertices of the graph are unknown. It is shown that through a proper choice of the parameters of the proposed algorithms, one can make the probability of finding minimum vertex cover in a stochastic graph as close to unity as possible. Experimental results on synthetic stochastic graphs reveal that at a certain confidence level the proposed algorithms significantly outperform the standard sampling method in terms of the number of samples needed to be taken from the vertices of the stochastic graph.     

层次序列索引的大规模动态标签图子图查询

标签图常用于智能交通网、生物信息网等新兴领域的建模。子图查询作为图数据分析的关键问题，引起了研究者的广泛关注。对现有子图查询算法的研究发现，随着图数据规模增大且频繁更新，传统子图查询算法普遍存在查询效率低，存储开销大，忽略顶点标签信息等问题。为此，提出了一种支持大规模动态标签图子图查询的层次序列索引（Dynamic Hierarchical Sequence，DHS），该索引提取数据图中带有顶点编号的层次拓扑序列关系以实现子图查询；针对图的动态变化，提出了更新点拓扑扩展式索引维护策略，仅从局部变化顶点及边开始进行增量式更新，大大降低了重建索引造成的巨大开销；提出了基于DHS索引的子图查询方法，仅需将查询图与数据图的层次序列进行匹配即可获得候选集，并在其上利用关系匹配策略获得最终查询结果。实验证明提出的方法在保证高效查询的同时降低了索引的创建及维护时间，提高了子图查询效率。     

关于互连网络的几个猜想

n-立方体是著名的互连网络,星图、煎饼图和冒泡排序图是由凯莱图模型设计出来的重要的互连网络。对换树（transposition tree）的凯莱图是一类特殊的凯莱图,星图和冒泡排序图分别是对换树为星和路的凯莱图。给出了关于n-立方体、星图、煎饼图、冒泡排序图和对换树的凯莱图的各一个猜想;提出了对换图的凯莱图的概念,进而由这一概念设计出了两个互连网络——圈图和轮图,并证明冒泡排序图和星图分别可嵌入圈图和轮图。     

A distance measure for large graphs based on prime graphs

Graphs are universal modeling tools. They are used to represent objects and their relationships in almost all domains: they are used to represent DNA, images, videos, social networks, XML documents, etc. When objects are represented by graphs, the problem of their comparison is a problem of comparing graphs. Comparing objects is a key task in our daily life. It is the core of a search engine, the backbone of a mining tool, etc. Nowadays, comparing objects faces the challenge of the large amount of data that this task must deal with. Moreover, when graphs are used to model these objects, it is known that graph comparison is very complex and computationally hard especially for large graphs. So, research on simplifying graph comparison gainedan interest and several solutions are proposed. In this paper, we explore and evaluate a new solution for the comparison of large graphs. Our approach relies on a compact encoding of graphs called prime graphs. Prime graphs are smaller and simpler than the original ones but they retain the structure and properties of the encoded graphs. We propose to approximate the similarity between two graphs by comparing the corresponding prime graphs. Simulations results show that this approach is effective for large graphs.     

特殊图的图修正问题研究综述

图修正问题是指在一个图中进行删除点、删除边或加边操作,使这个图转变成另一个具有某种特殊性质的图。图修正问题一直被广泛研究,尤其对弦图、区间图以及单位区间图的图修正问题的研究更是如此。弦图是完美图中最重要的一类图,也是(单位)区间图的父类图,很多经典的NP难问题在弦图上都是多项式可解的。区间图以及单位区间图在生物计算上有着广泛的应用。对这几类图的图修正问题的研究对计算机理论和实践有很大的贡献。首先介绍并总结了关于弦图、区间图以及单位区间图的图修正问题的重要算法和技术,然后对这些问题的研究现状进行分析,并提出了今后研究中值得关注的问题。     

基于结构图的手绘草图检索

提出一种基于结构图的草图检索方法,在保持图像大致形状的基础上对图像的轮廓数据进行有效的降维处理,解决了轮廓的起点选择、旋转、平移以及缩放等不变性,形成了图像的标准化形状描述子,并生成相应的结构图,提取结构图的四种特征,分别进行形似性度量。实验表明文中方法能够用来有效地进行草图检索。     

一种结合聚集图嵌入的社会化推荐算法

社交网络信息已被广泛的应用到传统的推荐上,一定程度上减轻了数据稀疏和冷启动问题.随着表示学习的兴起,出现了利用表示学习进行推荐的算法研究.然而社交网络过大,表示学习可扩展性差,难以在有限内存中进行计算.聚集图通过空间压缩,保留了关键的结构关系,去除次要或噪音的结构数据,便于表示学习能够有效学习图结构,从而更好地找到相似用户进行推荐.首先,利用图聚集算法同时考虑分组间及分组内的结构得到最终的聚集图;其次,在聚集图上计算随机游走的转移概率,然后选择每个具有偏差概率的后继节点并生成节点序列;最后将节点序列输入到skip-gram学习用户的潜在表示,获得节点的表示向量整合其信息到贝叶斯个性化排序模型(BPR)来解决项目排名问题.实验结果表明,该方法相比于社会化贝叶斯个性化排序(SBPR)、协同用户网络嵌入(CUNE)等基线方法在推荐任务中保持时间效率的同时有效提升了准确率、召回率和平均精度均值.     

Visual Analysis of Large Graphs: State‐of‐the‐Art and Future Research Challenges

The analysis of large graphs plays a prominent role in various fields of research and is relevant in many important application areas. Effective visual analysis of graphs requires appropriate visual presentations in combination with respective user interaction facilities and algorithmic graph analysis methods. How to design appropriate graph analysis systems depends on many factors, including the type of graph describing the data, the analytical task at hand and the applicability of graph analysis methods. The most recent surveys of graph visualization and navigation techniques cover techniques that had been introduced until 2000 or concentrate only on graph layouts published until 2002. Recently, new techniques have been developed covering a broader range of graph types, such as time‐varying graphs. Also, in accordance with ever growing amounts of graph‐structured data becoming available, the inclusion of algorithmic graph analysis and interaction techniques becomes increasingly important. In this State‐of‐the‐Art Report, we survey available techniques for the visual analysis of large graphs. Our review first considers graph visualization techniques according to the type of graphs supported. The visualization techniques form the basis for the presentation of interaction approaches suitable for visual graph exploration. As an important component of visual graph analysis, we discuss various graph algorithmic aspects useful for the different stages of the visual graph analysis process. We also present main open research challenges in this field.     

Estimating graph distance and centrality on shared nothing architectures

We present a parallel toolkit for pairwise distance computation in massive networks. Computing the exact shortest paths between a large number of vertices is a costly operation, and serial algorithms are not practical for billion‐scale graphs. We first describe an efficient parallel method to solve the single source shortest path problem on commodity hardware with no shared memory. Using it as a building block, we introduce a new parallel algorithm to estimate the shortest paths between arbitrary pairs of vertices. Our method exploits data locality, produces highly accurate results, and allows batch computation of shortest paths with 7% average error in graphs that contain billions of edges. The proposed algorithm is up to two orders of magnitude faster than previously suggested algorithms and does not require large amounts of memory or expensive high‐end servers. We further leverage this method to estimate the closeness and betweenness centrality metrics, which involve systems challenges dealing with indexing, joining, and comparing large datasets efficiently. In one experiment, we mined a real‐world Web graph with 700 million nodes and 12 billion edges to identify the most central vertices and calculated more than 63 billion shortest paths in 6 h on a 20‐node commodity cluster. Copyright © 2014 John Wiley & Sons, Ltd.     

Graph matching and clustering using spectral partitions

Although inexact graph-matching is a problem of potentially exponential complexity, the problem may be simplified by decomposing the graphs to be matched into smaller subgraphs. If this is done, then the process may cast into a hierarchical framework and hence rendered suitable for parallel computation. In this paper we describe a spectral method which can be used to partition graphs into non-overlapping subgraphs. In particular, we demonstrate how the Fiedler-vector of the Laplacian matrix can be used to decompose graphs into non-overlapping neighbourhoods that can be used for the purposes of both matching and clustering.