Route Visualization Using Detail Lenses

We present a method designed to address some limitations of typical route map displays of driving directions. The main goal of our system is to generate a printable version of a route map that shows the overview and detail views of the route within a single, consistent visual frame. Our proposed visualization provides a more intuitive spatial context than a simple list of turns. We present a novel multifocus technique to achieve this goal, where the foci are defined by points of interest (POI) along the route. A detail lens that encapsulates the POI at a finer geospatial scale is created for each focus. The lenses are laid out on the map to avoid occlusion with the route and each other, and to optimally utilize the free space around the route. We define a set of layout metrics to evaluate the quality of a lens layout for a given route map visualization. We compare standard lens layout methods to our proposed method and demonstrate the effectiveness of our method in generating aesthetically pleasing layouts. Finally, we perform a user study to evaluate the effectiveness of our layout choices.     

Visualization of graph products

Graphs are a versatile structure and abstraction for binary relationships between objects. To gain insight into such relationships, their corresponding graph can be visualized. In the past, many classes of graphs have been defined, e.g. trees, planar graphs, directed acyclic graphs, and visualization algorithms were proposed for these classes. Although many graphs may only be classified as "general" graphs, they can contain substructures that belong to a certain class. Archambault proposed the TopoLayout framework: rather than draw any arbitrary graph using one method, split the graph into components that are homogeneous with respect to one graph class and then draw each component with an algorithm best suited for this class. Graph products constitute a class that arises frequently in graph theory, but for which no visualization algorithm has been proposed until now. In this paper, we present an algorithm for drawing graph products and the aesthetic criterion graph product's drawings are subject to. We show that the popular High-Dimensional Embedder approach applied to cartesian products already respects this aestetic criterion, but has disadvantages. We also present how our method is integrated as a new component into the TopoLayout framework. Our implementation is used for further research of graph products in a biological context.     

GO: A cluster algorithm for graph visualization

As we are in the big data age, graph data such as user networks in Facebook and Flickr becomes large. How to reduce the visual complexity of a graph layout is a challenging problem. Clustering graphs is regarded as one of effective ways to address this problem. Most of current graph visualization systems, however, directly use existing clustering algorithms that are not originally developed for the visualization purpose. For graph visualization, a clustering algorithm should meet specific requirements such as the sufficient size of clusters, and automatic determination of the number of clusters. After identifying the requirements of clustering graphs for visualization, in this paper we present a new clustering algorithm that is particularly designed for visualization so as to reduce the visual complexity of a layout, together with a strategy for improving the scalability of our algorithm. Experiments have demonstrated that our proposed algorithm is capable of detecting clusters in a way that is required in graph visualization.     

Smashing peacocks further: drawing quasi-trees from biconnected components

We extend the popular force-directed approach to network (or graph) layout to allow separation constraints, which enforce a minimum horizontal or vertical separation between selected pairs of nodes. This simple class of linear constraints is expressive enough to satisfy a wide variety of application-specific layout requirements, including: layout of directed graphs to better show flow; layout with non-overlapping node labels; and layout of graphs with grouped nodes (called clusters). In the stress majorization force-directed layout process, separation constraints can be treated as a quadratic programming problem. We give an incremental algorithm based on gradient projection for efficiently solving this problem. The algorithm is considerably faster than using generic constraint optimization techniques and is comparable in speed to unconstrained stress majorization. We demonstrate the utility of our technique with sample data from a number of practical applications including gene-activation networks, terrorist networks and visualization of high-dimensional data     

面向层次化数据的变分圆形树图

圆形树图(circular treemap)是面向层次化数据的一种信息可视化方法.提出一种圆形树图构造方法,将圆形树图的布局问题与组合优化中的圆排列(disk packing)问题相结合,以一种基于变分连续优化的算法求解多个半径不同圆的优化布局,由此提高圆形树图的空间利用率,并支持层次下行、层次上行与焦点+上下文等自然交互方式.实验结果表明了该方法的有效性.     

基于图匹配的分层布局算法

针对节点数目较大并且度数比较平均的无向图,根据分层扩展的思想,提出一种基于图匹配的分层布局算法（Graph Matching Hierarchy,GMH）。基于图匹配思想对大图进行递归化简,然后应用FR算法对最粗化图进行布局,最后利用质心布局算法对图进行扩展。实验结果表明,GMH算法能够提高可视化效率,改善布局效果,且分层布局的结果更易于理解。      

FMR:基于FR的快速多层次算法

图可视化技术是可视化研究的重要内容,近年来大图的绘制问题一直是图可视化 技术的焦点。为此,提出了一种快速多层次算法用于解决大图绘制问题。采用多层次方法作为 算法的框架,以 FR 力导向算法的变体结合质心算法以及四叉树空间分解等方法对单层布局进 行优化。另外,还使用了约束规范化和能量模型 2 种加速方法。实验表明,该算法具有高效的 性能和良好的布局效果。其效率非常高,在单核 CPU 下,可以在大约 5 s 内很好地绘制出 10 000 个顶点的图。并与几种经典的算法进行了比较,也证明了该算法的有效性和实用性。此外,该 算法易于实现,可被轻易推广到其他布局算法上,以加速其运算。     

A stable graph layout algorithm for processes

Process mining enables organizations to analyze data about their (business) processes. Visualization is key to gaining insight into these processes and the associated data. Process visualization requires a high‐quality graph layout that intuitively represents the semantics of the process. Process analysis additionally requires interactive filtering to explore the process data and process graph. The ideal process visualization therefore provides a high‐quality, intuitive layout and preserves the mental map of the user during the visual exploration. The current industry standard used for process visualization does not satisfy either of these requirements. In this paper, we propose a novel layout algorithm for processes based on the Sugiyama framework. Our approach consists of novel ranking and order constraint algorithms and a novel crossing minimization algorithm. These algorithms make use of the process data to compute stable, high‐quality layouts. In addition, we use phased animation to further improve mental map preservation. Quantitative and qualitative evaluations show that our approach computes layouts of higher quality and preserves the mental map better than the industry standard. Additionally, our approach is substantially faster, especially for graphs with more than 250 edges.     

Unfolding Edges: Adding Context to Edges in Multivariate Graph Visualization

Existing work on visualizing multivariate graphs is primarily concerned with representing the attributes of nodes. Even though edges are the constitutive elements of networks, there have been only few attempts to visualize attributes of edges. In this work, we focus on the critical importance of edge attributes for interpreting network visualizations and building trust in the underlying data. We propose ‘unfolding of edges’ as an interactive approach to integrate multivariate edge attributes dynamically into existing node-link diagrams. Unfolding edges is an in-situ approach that gradually transforms basic links into detailed representations of the associated edge attributes. This approach extends focus+context, semantic zoom, and animated transitions for network visualizations to accommodate edge details on-demand without cluttering the overall graph layout. We explore the design space for the unfolding of edges, which covers aspects of making space for the unfolding, of actually representing the edge context, and of navigating between edges. To demonstrate the utility of our approach, we present two case studies in the context of historical network analysis and computational social science. For these, web-based prototypes were implemented based on which we conducted interviews with domain experts. The experts' feedback suggests that the proposed unfolding of edges is a useful tool for exploring rich edge information of multivariate graphs.     

一种用于Marching-Graph图形绘制的快速收敛布局算法

Marching-Graph是一种将图形隐喻技术和空间隐喻技术集成为一体的新的可视化方法.它为用户提供了高度可交互性地图,使用户可访问那些具有地理属性的信息的逻辑结构.它通过有效的人图交互和跨空间浏览为用户提供了一种可视分析和挖掘未知信息的机制,而不是将已知的信息呈现在地图上.然而,传统的力导向布局算法在达到力量均衡配置方面非常慢.为使一个图形布局收敛,它们通常需花费几十秒的时间.因此。当用户快速行进于地理区间时,那些力导向布局算法就不能满足快速绘制一系列图形的要求.提出了一种快速收敛布局方法,当用户在Marching-Graph中通过力导向布局逐步探究一系列图形时,它可以加速交互时间.通过结合辐射树绘图技术和力导向图形绘制方法来取得能量最小化的快速收敛.     

Stereoscopic highlighting: 2D graph visualization on stereo displays

In this paper we present a new technique and prototype graph visualization system, stereoscopic highlighting, to help answer accessibility and adjacency queries when interacting with a node-link diagram. Our technique utilizes stereoscopic depth to highlight regions of interest in a 2D graph by projecting these parts onto a plane closer to the viewpoint of the user. This technique aims to isolate and magnify specific portions of the graph that need to be explored in detail without resorting to other highlighting techniques like color or motion, which can then be reserved to encode other data attributes. This mechanism of stereoscopic highlighting also enables focus+context views by juxtaposing a detailed image of a region of interest with the overall graph, which is visualized at a further depth with correspondingly less detail. In order to validate our technique, we ran a controlled experiment with 16 subjects comparing static visual highlighting to stereoscopic highlighting on 2D and 3D graph layouts for a range of tasks. Our results show that while for most tasks the difference in performance between stereoscopic highlighting alone and static visual highlighting is not statistically significant, users performed better when both highlighting methods were used concurrently. In more complicated tasks, 3D layout with static visual highlighting outperformed 2D layouts with a single highlighting method. However, it did not outperform the 2D layout utilizing both highlighting techniques simultaneously. Based on these results, we conclude that stereoscopic highlighting is a promising technique that can significantly enhance graph visualizations for certain use cases.     

基于力导向模型的网络图自动布局算法综述

实现网络图形中节点和边自动布局一直是可视化研究中一个重要内容,基于力导向模型的自动布局算法则是该类研究中应用最广、文献最多的一类方法。根据研究方向出现的时间顺序,从基本模型、基于多维尺度分析的布局算法、多层迭代布局算法、非欧空间节点布局算法、受约束图形自动布局算法等五个方面对基于力引导模型的网络图自动布局算法的典型方法、研究进展、分支情况等进行了描述,并对发展前沿进行了讨论。     

Volume-based large dynamic graph analysis supported by evolution provenance

We present an approach for the visualization and interactive analysis of dynamic graphs that contain a large number of time steps. A specific focus is put on the support of analyzing temporal aspects in the data. Central to our approach is a static, volumetric representation of the dynamic graph based on the concept of space-time cubes that we create by stacking the adjacency matrices of all time steps. The use of GPU-accelerated volume rendering techniques allows us to render this representation interactively. We identified four classes of analytics methods as being important for the analysis of large and complex graph data, which we discuss in detail: data views, aggregation and filtering, comparison, and evolution provenance. Implementations of the respective methods are presented in an integrated application, enabling interactive exploration and analysis of large graphs. We demonstrate the applicability, usefulness, and scalability of our approach by presenting two examples for analyzing dynamic graphs. Furthermore, we let visualization experts evaluate our analytics approach.

     

A space-filling visualization technique for multivariate small-world graphs

We introduce an information visualization technique, known as GreenCurve, for large multivariate sparse graphs that exhibit small-world properties. Our fractal-based design approach uses spatial cues to approximate the node connections and thus eliminates the links between the nodes in the visualization. The paper describes a robust algorithm to order the neighboring nodes of a large sparse graph by solving the Fiedler vector of its graph Laplacian, and then fold the graph nodes into a space-filling fractal curve based on the Fiedler vector. The result is a highly compact visualization that gives a succinct overview of the graph with guaranteed visibility of every graph node. GreenCurve is designed with the power grid infrastructure in mind. It is intended for use in conjunction with other visualization techniques to support electric power grid operations. The research and development of GreenCurve was conducted in collaboration with domain experts who understand the challenges and possibilities intrinsic to the power grid infrastructure. The paper reports a case study on applying GreenCurve to a power grid problem and presents a usability study to evaluate the design claims that we set forth.     

TreeNetViz: revealing patterns of networks over tree structures

Network data often contain important attributes from various dimensions such as social affiliations and areas of expertise in a social network. If such attributes exhibit a tree structure, visualizing a compound graph consisting of tree and network structures becomes complicated. How to visually reveal patterns of a network over a tree has not been fully studied. In this paper, we propose a compound graph model, TreeNet, to support visualization and analysis of a network at multiple levels of aggregation over a tree. We also present a visualization design, TreeNetViz, to offer the multiscale and cross-scale exploration and interaction of a TreeNet graph. TreeNetViz uses a Radial, Space-Filling (RSF) visualization to represent the tree structure, a circle layout with novel optimization to show aggregated networks derived from TreeNet, and an edge bundling technique to reduce visual complexity. Our circular layout algorithm reduces both total edge-crossings and edge length and also considers hierarchical structure constraints and edge weight in a TreeNet graph. These experiments illustrate that the algorithm can reduce visual cluttering in TreeNet graphs. Our case study also shows that TreeNetViz has the potential to support the analysis of a compound graph by revealing multiscale and cross-scale network patterns.     

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.     

Visual analysis of multivariate state transition graphs

We present a new approach for the visual analysis of state transition graphs. We deal with multivariate graphs where a number of attributes are associated with every node. Our method provides an interactive attribute-based clustering facility. Clustering results in metric, hierarchical and relational data, represented in a single visualization. To visualize hierarchically structured quantitative data, we introduce a novel technique: the bar tree. We combine this with a node-link diagram to visualize the hierarchy and an arc diagram to visualize relational data. Our method enables the user to gain significant insight into large state transition graphs containing tens of thousands of nodes. We illustrate the effectiveness of our approach by applying it to a real-world use case. The graph we consider models the behavior of an industrial wafer stepper and contains 55 043 nodes and 289 443 edges     

Customizing a Fisheye View Algorithm to Preserve the Mental Map

Frequently, large knowledge bases are represented by graphs. Many visualization tools allow users or other applications to interact with and adjust the layouts of these graphs. One layout adjustment problem is that of showing more detail without eliding parts of the graph. Approaches based on a fisheye lens paradigm seem well suited to this task. However, many of these techniques are non-trivial to implement and their distortion techniques often cannot be altered to suit different graph layouts. When distorting a graph layout, it is often desirable to preserve various properties of the original graph in an adjusted view. Pertinent properties may include straightness of lines, graph topology, orthogonalities and proximities. However, it is normally not possible to preserve all of the original properties of the graph layout. The type of layout and its application should be considered when deciding which properties to preserve or distort. This paper describes a fisheye view algorithm which can be customized to suit various different graph layouts. In contrast to other methods, the user can select which properties of the original graph layout to preserve in an adjusted view. The technique is demonstrated through its application to visualizing structures in large software systems.     

A tabu search based approach for graph layout

This paper describes an automated tabu search based method for drawing general graph layouts with straight lines. To our knowledge, this is the first time tabu methods have been applied to graph drawing. We formulated the task as a multi-criteria optimization problem with a number of metrics which are used in a weighted fitness function to measure the aesthetic quality of the graph layout. The main goal of this work is to speed up the graph layout process without sacrificing layout quality. To achieve this, we use a tabu search based method that goes through a predefined number of iterations to minimize the value of the fitness function. Tabu search always chooses the best solution in the neighbourhood. This may lead to cycling, so a tabu list is used to store moves that are not permitted, meaning that the algorithm does not choose previous solutions for a set period of time. We evaluate the method according to the time spent to draw a graph and the quality of the drawn graphs. We give experimental results applied on random graphs and we provide statistical evidence that our method outperforms a fast search-based drawing method (hill climbing) in execution time while it produces comparably good graph layouts. We also demonstrate the method on real world graph datasets to show that we can reproduce similar results in a real world setting.