Pathfinder: Visual Analysis of Paths in Graphs

The analysis of paths in graphs is highly relevant in many domains. Typically, path‐related tasks are performed in node‐link layouts. Unfortunately, graph layouts often do not scale to the size of many real world networks. Also, many networks are multivariate, i.e., contain rich attribute sets associated with the nodes and edges. These attributes are often critical in judging paths, but directly visualizing attributes in a graph layout exacerbates the scalability problem. In this paper, we present visual analysis solutions dedicated to path‐related tasks in large and highly multivariate graphs. We show that by focusing on paths, we can address the scalability problem of multivariate graph visualization, equipping analysts with a powerful tool to explore large graphs. We introduce Pathfinder, a technique that provides visual methods to query paths, while considering various constraints. The resulting set of paths is visualized in both a ranked list and as a node‐link diagram. For the paths in the list, we display rich attribute data associated with nodes and edges, and the node‐link diagram provides topological context. The paths can be ranked based on topological properties, such as path length or average node degree, and scores derived from attribute data. Pathfinder is designed to scale to graphs with tens of thousands of nodes and edges by employing strategies such as incremental query results. We demonstrate Pathfinder's fitness for use in scenarios with data from a coauthor network and biological pathways.     

Node and edge selectivity estimation for range queries in spatial networks

Modern applications requiring spatial network processing pose several interesting query optimization challenges. Spatial networks are usually represented as graphs, and therefore, queries involving a spatial network can be executed by using the corresponding graph representation. This means that the cost for executing a query is determined by graph properties such as the graph order and size (i.e., number of nodes and edges) and other graph parameters. In this paper, we present novel methods to estimate the number of nodes and edges in regions of interest in spatial networks, towards predicting the space and time requirements for range queries. The methods are evaluated by using real-life and synthetic data sets. Experimental results show that the number of nodes and edges can be estimated efficiently and accurately, with relatively small space requirements, thus providing useful information to the query optimizer.     

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.     

ImPrEd: An Improved Force‐Directed Algorithm that Prevents Nodes from Crossing Edges

PrEd [ [Ber00] ] is a force‐directed algorithm that improves the existing layout of a graph while preserving its edge crossing properties. The algorithm has a number of applications including: improving the layouts of planar graph drawing algorithms, interacting with a graph layout, and drawing Euler‐like diagrams. The algorithm ensures that nodes do not cross edges during its execution. However, PrEd can be computationally expensive and overly‐restrictive in terms of node movement. In this paper, we introduce ImPrEd: an improved version of PrEd that overcomes some of its limitations and widens its range of applicability. ImPrEd also adds features such as flexible or crossable edges, allowing for greater control over the output. Flexible edges, in particular, can improve the distribution of graph elements and the angular resolution of the input graph. They can also be used to generate Euler diagrams with smooth boundaries. As flexible edges increase data set size, we experience an execution/drawing quality trade off. However, when flexible edges are not used, ImPrEdproves to be consistently faster than PrEd.     

Apex graph grammars and attribute grammars

Summary Apex graph grammars are a particular type of directed node-label controlled (DNLC) graph grammars: the embedding edges are established between terminal nodes only. Apex graph grammars, slightly generalized, can generate the sets of dependency graphs of attribute grammars. The other way around, every apex graph language can be obtained from such a dependency graph language by a graph replacement (which is an operation analogous to a string homomorphism).     

Real‐time cutting simulation of meshless deformable object using dynamic bounding volume hierarchy

This paper proposes a novel method for a real‐time cutting simulation of deformable objects using meshless method. The method utilizes a rapid refinement of topological relations among the simulation nodes of meshless deformable objects. Topological relations are defined as an undirected graph based on a visibility criterion. The graph connects the adjacent nodes that lie within a support of each node. The topological relations are refined by removing the edges of the graph that is intersected by the cut surface during the cutting simulation. Our approach utilizes a bounding volume hierarchy (BVH) to accelerate the computation of the intersection test. The BVH reconstruction algorithm is proposed to account for the cases where pieces of the object are completely cut out from the object. Algorithms to examine the connectivity among simulation nodes and accordingly reconstructing the BVH using two‐level BVH are presented. The proposed approach achieves real‐time cutting simulation of deformable objects through the rapid refinement of the topological relation. In addition, the computational performance of the cutting procedure is preserved during the entire simulation, thanks to the real‐time reconstruction of the BVH. Copyright © 2012 John Wiley & Sons, Ltd.     

改进的k度匿名图构造算法

在社交网络中, 为防范用户隐私泄漏, 在用户数据发布前需要做匿名化处理. 针对以节点度数为背景知识的隐私攻击, 将社交网络匿名化问题建模为图的k度匿名化问题; 其主要方法是对图添加尽可能少的边或点来满足度匿名化要求, 其中要求添加边或点较少是期望尽可能保持原图结构特性. 目前, 加边类算法并不能很好地保留平均路径长度等结构特性; 加边且可加点类算法尽管能更好地保留原图结构特性, 但添加的边或点较多. 本文融合两类算法的策略提出改进算法. 新算法利用贪心法生成匿名度序列, 然后基于社区结构加边, 并且优先满足其匿名代价高于平均匿名代价的节点的匿名化要求; 若加边不能完成匿名化, 则通过加点实现图匿名化. 真实数据集上的实验结果表明新算法能更好地保留图的几种典型的结构特性, 并且添加的边或点更少.     

Time Series Prediction for Graphs in Kernel and Dissimilarity Spaces

Graphs are a flexible and general formalism providing rich models in various important domains, such as distributed computing, intelligent tutoring systems or social network analysis. In many cases, such models need to take changes in the graph structure into account, that is, changes in the number of nodes or in the graph connectivity. Predicting such changes within graphs can be expected to yield important insight with respect to the underlying dynamics, e.g. with respect to user behaviour. However, predictive techniques in the past have almost exclusively focused on single edges or nodes. In this contribution, we attempt to predict the future state of a graph as a whole. We propose to phrase time series prediction as a regression problem and apply dissimilarity- or kernel-based regression techniques, such as 1-nearest neighbor, kernel regression and Gaussian process regression, which can be applied to graphs via graph kernels. The output of the regression is a point embedded in a pseudo-Euclidean space, which can be analyzed using subsequent dissimilarity- or kernel-based processing methods. We discuss strategies to speed up Gaussian processes regression from cubic to linear time and evaluate our approach on two well-established theoretical models of graph evolution as well as two real data sets from the domain of intelligent tutoring systems. We find that simple regression methods, such as kernel regression, are sufficient to capture the dynamics in the theoretical models, but that Gaussian process regression significantly improves the prediction error for real-world data.     

Perceptual organization in user-generated graph layouts

Many graph layout algorithms optimize visual characteristics to achieve useful representations. Implicitly, their goal is to create visual representations that are more intuitive to human observers. In this paper, we asked users to explicitly manipulate nodes in a network diagram to create layouts that they felt best captured the relationships in the data. This allowed us to measure organizational behavior directly, allowing us to evaluate the perceptual importance of particular visual features, such as edge crossings and edge-lengths uniformity. We also manipulated the interior structure of the node relationships by designing data sets that contained clusters, that is, sets of nodes that are strongly interconnected. By varying the degree to which these clusters were "masked" by extraneous edges we were able to measure observers' sensitivity to the existence of clusters and how they revealed them in the network diagram. Based on these measurements we found that observers are able to recover cluster structure, that the distance between clusters is inversely related to the strength of the clustering, and that users exhibit the tendency to use edges to visually delineate perceptual groups. These results demonstrate the role of perceptual organization in representing graph data and provide concrete recommendations for graph layout algorithms.     

Link classification with probabilistic graphs

The need to deal with the inherent uncertainty in real-world relational or networked data leads to the proposal of new probabilistic models, such as probabilistic graphs. Every edge in a probabilistic graph is associated with a probability whose value represents the likelihood of its existence, or the strength of the relation between the entities it connects. The aim of this paper is to propose two machine learning techniques for the link classification problem in relational data exploiting the probabilistic graph representation. Both the proposed methods will exploit a language-constrained reachability method to infer the probability of possible hidden relationships that may exists between two nodes in a probabilistic graph. Each hidden relationships between two nodes may be viewed as a feature (or a factor), and its corresponding probability as its weight, while an observed relationship is considered as a positive instance for its corresponding link label. Given a training set of observed links, the first learning approach is to use a propositionalization technique adopting a L2-regularized Logistic Regression to learn a model able to predict unobserved link labels. Since in some cases the edges’ probability may be not known in advance or they could not be precisely defined for a classification task, the second xposed approach is to exploit the inference method and to use a mean squared technique to learn the edges’ probabilities. Both the proposed methods have been evaluated on real world data sets and the corresponding results proved their validity.     

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。     

A graph-theoretic language extension for an interactive computer graphics environment

A programming language extension, AGILE, for the processing of graphs within an interactive computer graphics environment, is defined. The language is intended to be used for expressing and illustrating graph-theoretic algorithms and applications. However it does not deal with the actual drawing or display of graphs; rather one is able to access an existing general-purpose graphics package. The language then is intended to be used, in conjunction with a graphics package, as a tool for the production of more specialised graphics systems: the language allows one to naturally exploit the underlying graph structure found in a wide class of problems, while a graphics environment permits the elegant display of (and interaction with) such representations.AGILE extends the host language, C, by the addition of a graph database, and operators and control structures to manipulate this database. The graph structure is composed of five basic types: nodes, edges, graphs, sets and bugs (references). A general set of operators and tests are provided, including those for entity creation and deletion, node and edge traversal and tests for equality and containment of sets and graphs. Edges may be treated as being either directed or undirected; also multiple edges between nodes and self-loops are allowed. Arbitrary values and properties may be associated with each of the basic types. In particular, since a node may have a graph as value, a graph hierarchy is possible. Graphics primitives are provided by the GPAC graphics system.Three substantial applications have been programmed in the language: a system for producing diagrams of graphs and a class of data structures, a system for animating four algorithms for finding the maximum flow in a network, and a system for animating and making films of systems dynamics models.Several examples of programmes written in AGILE are included.     

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     

基于最优传输的层次化图核

已有的图核大多关注图的局部属性,利用局部的拓扑特征构建图的相似性度量,忽略图的层次结构信息.为了解决这个问题,文中提出基于最优传输的层次化图核.首先,将每个图表示成层次化的图结构.在层次化图结构构建过程中,利用K-means聚类算法构造每层图的节点,节点间的概率连接作为图的边.然后,利用带有熵约束的最优传输计算两图的层次结构上每层图之间的最优传输距离.最后,基于最优传输距离计算基于最优传输的层次化图核.在6个真实图数据集上的实验表明,文中方法可提升分类性能.     

Semi-supervised classification and betweenness computation on large, sparse, directed graphs

This work addresses graph-based semi-supervised classification and betweenness computation in large, sparse, networks (several millions of nodes). The objective of semi-supervised classification is to assign a label to unlabeled nodes using the whole topology of the graph and the labeling at our disposal. Two approaches are developed to avoid explicit computation of pairwise proximity between the nodes of the graph, which would be impractical for graphs containing millions of nodes. The first approach directly computes, for each class, the sum of the similarities between the nodes to classify and the labeled nodes of the class, as suggested initially in [1] and [2]. Along this approach, two algorithms exploiting different state-of-the-art kernels on a graph are developed. The same strategy can also be used in order to compute a betweenness measure. The second approach works on a trellis structure built from biased random walks on the graph, extending an idea introduced in [3]. These random walks allow to define a biased bounded betweenness for the nodes of interest, defined separately for each class. All the proposed algorithms have a linear computing time in the number of edges while providing good results, and hence are applicable to large sparse networks. They are empirically validated on medium-size standard data sets and are shown to be competitive with state-of-the-art techniques. Finally, we processed a novel data set, which is made available for benchmarking, for multi-class classification in a large network: the U.S. patents citation network containing 3M nodes (of six different classes) and 38M edges. The three proposed algorithms achieve competitive results (around 85% classification rate) on this large network-they classify the unlabeled nodes within a few minutes on a standard workstation.     

Layered data association using graph-theoretic formulation with applications to tennis ball tracking in monocular sequences

In this paper, we propose a multi-layered data association scheme with graph-theoretic formulation for tracking multiple objects that undergo switching dynamics in clutter. The proposed scheme takes as input object candidates detected in each frame. At the object candidate level, "tracklets' are "grown' from sets of candidates that have high probabilities of containing only true positives. At the tracklet level, a directed and weighted graph is constructed, where each node is a tracklet, and the edge weight between two nodes is defined according to the "compatibility' of the two tracklets. The association problem is then formulated as an all-pairs shortest path (APSP) problem in this graph. Finally, at the path level, by analyzing the all-pairs shortest paths, all object trajectories are identified, and track initiation and track termination are automatically dealt with. By exploiting a special topological property of the graph, we have also developed a more efficient APSP algorithm than the general-purpose ones. The proposed data association scheme is applied to tennis sequences to track tennis balls. Experiments show that it works well on sequences where other data association methods perform poorly or fail completely.     

TopoLayout: multilevel graph layout by topological features

We describe TopoLayout, a feature-based, multilevel algorithm that draws undirected graphs based on the topological features they contain. Topological features are detected recursively inside the graph, and their subgraphs are collapsed into single nodes, forming a graph hierarchy. Each feature is drawn with an algorithm tuned for its topology. As would be expected from a feature-based approach, the runtime and visual quality of TopoLayout depends on the number and types of topological features present in the graph. We show experimental results comparing speed and visual quality for TopoLayout against four other multilevel algorithms on a variety of data sets with a range of connectivities and sizes. TopoLayout frequently improves the results in terms of speed and visual quality on these data sets     

DBORank:对象级别的关系数据库信息检索方法

对象级别的信息检索已经引起越来越多的关注和研究。针对这一研究问题,设计并实现了一个对象级别的关系数据库信息检索方法DBORank,来有效提高关系数据库信息检索效果。DBORank方法从数据库和信息检索两个角度出发,设计了一种灵活有效的评分机制,它既考虑了对象级别数据图的链接结构,又考虑了图中对象结点的内部结构,边的类型和权值,对象内容相关性等因素,同时优化了对象评分的迭代算法。实验表明DBORank方法具有良好的检索效果和效率。