Image‐Based Edge Bundles: Simplified Visualization of Large Graphs

We present a new approach aimed at understanding the structure of connections in edge‐bundling layouts. We combine the advantages of edge bundles with a bundle‐centric simplified visual representation of a graph's structure. For this, we first compute a hierarchical edge clustering of a given graph layout which groups similar edges together. Next, we render clusters at a user‐selected level of detail using a new image‐based technique that combines distance‐based splatting and shape skeletonization. The overall result displays a given graph as a small set of overlapping shaded edge bundles. Luminance, saturation, hue, and shading encode edge density, edge types, and edge similarity. Finally, we add brushing and a new type of semantic lens to help navigation where local structures overlap. We illustrate the proposed method on several real‐world graph datasets.     

Evaluating esthetics for user-sketched layouts of clustered graphs with known clustering information

This paper aims to empirically analyze the esthetics for user-sketched layouts of clustered graphs with known clustering information. In our experiments, given not only the adjacency list of a clustered graph but also its predefined clustering information, each participant was asked to manually sketch clustered graphs “nicely” from scratch on a tablet system using a stylus. Different from previous works, the main concern in this paper is on which graph drawing esthetics people favor when sketching their own drawings of clustered graphs with known clustering information. Another concern of this paper is on the esthetics of clustered graph layouts employed by participants which include not only characteristics and structures of the final graph layouts but also the behavior of user's sketching process (including layout creation and adjustment). By observing all layouts and drawing processes, the drawing strategies which participants applied and the drawing esthetics are analyzed. Results show that most participants were unsurprisingly able to draw graphs with clear presence of bridge edges and clustering cohesiveness; more importantly, to distinguish clusters within the restricted-size tablet screen during the drawing process, some of the participants were still able to make each cluster with fewer edge crossings, more symmetries, and more alignment of grid in a smaller drawing area where the cluster spreads. Our results support that to alleviate user's complex drawing tasks, aside from the grid-based editing function suggested by the previous work, graph drawing systems should also provide the clustering information if the structure of the graph to be drawn is known.     

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.     

Graph Layouts by t‐SNE

We propose a new graph layout method based on a modification of the t‐distributed Stochastic Neighbor Embedding (t‐SNE) dimensionality reduction technique. Although t‐SNE is one of the best techniques for visualizing high‐dimensional data as 2D scatterplots, t‐SNE has not been used in the context of classical graph layout. We propose a new graph layout method, tsNET, based on representing a graph with a distance matrix, which together with a modified t‐SNE cost function results in desirable layouts. We evaluate our method by a formal comparison with state‐of‐the‐art methods, both visually and via established quality metrics on a comprehensive benchmark, containing real‐world and synthetic graphs. As evidenced by the quality metrics and visual inspection, tsNET produces excellent layouts.     

Force-Directed Edge Bundling for Graph Visualization

Graphs depicted as node-link diagrams are widely used to show relationships between entities. However, node-link diagrams comprised of a large number of nodes and edges often suffer from visual clutter. The use of edge bundling remedies this and reveals high-level edge patterns. Previous methods require the graph to contain a hierarchy for this, or they construct a control mesh to guide the edge bundling process, which often results in bundles that show considerable variation in curvature along the overall bundle direction. We present a new edge bundling method that uses a self-organizing approach to bundling in which edges are modeled as flexible springs that can attract each other. In contrast to previous methods, no hierarchy is used and no control mesh. The resulting bundled graphs show significant clutter reduction and clearly visible high-level edge patterns. Curvature variation is furthermore minimized, resulting in smooth bundles that are easy to follow. Finally, we present a rendering technique that can be used to emphasize the bundling.     

Game level layout from design specification

The design of video game environments, or levels, aims to control gameplay by steering the player through a sequence of designer‐controlled steps, while simultaneously providing a visually engaging experience. Traditionally these levels are painstakingly designed by hand, often from pre‐existing building blocks, or space templates. In this paper, we propose an algorithmic approach for automatically laying out game levels from user‐specified blocks. Our method allows designers to retain control of the gameplay flow via user‐specified level connectivity graphs, while relieving them from the tedious task of manually assembling the building blocks into a valid, plausible layout. Our method produces sequences of diverse layouts for the same input connectivity, allowing for repeated replay of a given level within a visually different, new environment. We support complex graph connectivities and various building block shapes, and are able to compute complex layouts in seconds. The two key components of our algorithm are the use of configuration spaces defining feasible relative positions of building blocks within a layout and a graph‐decomposition based layout strategy that leverages graph connectivity to speed up convergence and avoid local minima. Together these two tools quickly steer the solution toward feasible layouts. We demonstrate our method on a variety of real‐life inputs, and generate appealing layouts conforming to user specifications.     

Aesthetics-based Graph Layout for Human Consumption

Automatic graph layout is an important and long-studied problem. The basic straight-edge graph layout problem is to find spatial positions for the nodes of an input graph that maximize some measure of desirability. When graph layout is intended for human consumption, we call this measure of desirability an aesthetic. We seek an algorithm that produces graph layouts of high aesthetic quality not only for general graphs, but also for specific classes of graphs, such as trees and directed acyclic graphs. The Aesthetic Graph Layout (AGLO) approach described in this paper models graph layout as a multiobjective optimization problem, where the value of a layout is determined by multiple user-controlled layout aesthetics. The current AGLO algorithm combines the power and flexibility of the simulated annealing approach of Davidson and Harel (1989) with the relative speed of the method of Fruchterman and Reingold (1991). In addition, it is more general, and incorporates several new layout aesthetics to support new layout styles. Using these aesthetics, we are able to produce pleasing displays for graphs on which these other methods flounder.     

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.     

Convergent drawing for mutually connected directed graphs

Directed graphs are used to represent a variety of datasets, including friendship on social networking services (SNS), pathways of genes, and citations of research papers. Graph drawing is useful in representing such datasets. At the international conference on Information Visualization (IV), we have presented a convergent edge drawing and a node layout technique for tightly and mutually connected directed graphs. The edge drawing technique in the IV paper includes three features: ordinary bundling of edges connecting pairs of node clusters, convergence of multiple bundles that connect to the same node cluster, and shape adjustment of two bundles connecting the same pair of node clusters. In this paper, we present improved node layout and edge drawing techniques, which make our edge bundling more effective. This paper also introduces a case study with a directed paper citation graph dataset.vvvvv     

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.     

RailwayDB: adaptive storage of interaction graphs

We are living in an ever more connected world, where data recording the interactions between people, software systems, and the physical world is becoming increasingly prevalent. These data often take the form of a temporally evolving graph, where entities are the vertices and the interactions between them are the edges. We call such graphs interaction graphs. Various domains, including telecommunications, transportation, and social media, depend on analytics performed on interaction graphs. The ability to efficiently support historical analysis over interaction graphs requires effective solutions for the problem of data layout on disk. This paper presents an adaptive disk layout called the railway layout for optimizing disk block storage for interaction graphs. The key idea is to divide blocks into one or more sub-blocks. Each sub-block contains the entire graph structure, but only a subset of the attributes. This improves query I/O, at the cost of increased storage overhead. We introduce optimal integer linear program (ILP) formulations for partitioning disk blocks into sub-blocks with overlapping and nonoverlapping attributes. Additionally, we present greedy heuristics that can scale better compared to the ILP alternatives, yet achieve close to optimal query I/O. We provide an implementation of the railway layout as part of RailwayDB—an open-source graph database we have developed. To demonstrate the benefits of the railway layout, we provide an extensive experimental evaluation, including model-based as well as empirical results comparing our approach to baseline alternatives.     

Using adjacency matrices to lay out larger small-world networks

Many networks exhibit small-world properties. The structure of a small-world network is characterized by short average path lengths and high clustering coefficients. Few graph layout methods capture this structure well which limits their effectiveness and the utility of the visualization itself. Here we present an extension to our novel graphTPP layout method for laying out small-world networks using only their topological properties rather than their node attributes. The Watts–Strogatz model is used to generate a variety of graphs with a small-world network structure. Community detection algorithms are used to generate six different clusterings of the data. These clusterings, the adjacency matrix and edgelist are loaded into graphTPP and, through user interaction combined with linear projections of the adjacency matrix, graphTPP is able to produce a layout which visually separates these clusters. These layouts are compared to the layouts of two force-based techniques. graphTPP is able to clearly separate each of the communities into a spatially distinct area and the edge relationships between the clusters show the strength of their relationship. As a secondary contribution, an edge-grouping algorithm for graphTPP is demonstrated as a means to reduce visual clutter in the layout and reinforce the display of the strength of the relationship between two communities.     

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.     

面向深度学习的批处理矩阵乘法设计与实现

本文设计并实现了面向深度学习的统一框架批处理矩阵乘法.我们细致地分析了利用矩阵乘法实现卷积的过程中卷积核、输入特征图和输出特征图在NCHW和NHWC两类存储格式下的矩阵数据排列特点,指出了其和矩阵行列主序的关系.在此基础上,为了更好复用共享的卷积核数据,我们提出将批量输入特征图转化为一个矩阵整体进行计算的方法.我们设计...     

The Perception of Graph Properties in Graph Layouts

When looking at drawings of graphs, questions about graph density, community structures, local clustering and other graph properties may be of critical importance for analysis. While graph layout algorithms have focused on minimizing edge crossing, symmetry, and other such layout properties, there is not much known about how these algorithms relate to a user's ability to perceive graph properties for a given graph layout. In this study, we apply previously established methodologies for perceptual analysis to identify which graph drawing layout will help the user best perceive a particular graph property. We conduct a large scale (n = 588) crowdsourced experiment to investigate whether the perception of two graph properties (graph density and average local clustering coefficient) can be modeled using Weber's law. We study three graph layout algorithms from three representative classes (Force Directed ‐ FD, Circular, and Multi‐Dimensional Scaling ‐ MDS), and the results of this experiment establish the precision of judgment for these graph layouts and properties. Our findings demonstrate that the perception of graph density can be modeled with Weber's law. Furthermore, the perception of the average clustering coefficient can be modeled as an inverse of Weber's law, and the MDS layout showed a significantly different precision of judgment than the FD layout.     

Geometry-based edge clustering for graph visualization

Graphs have been widely used to model relationships among data. For large graphs, excessive edge crossings make the display visually cluttered and thus difficult to explore. In this paper, we propose a novel geometry-based edge-clustering framework that can group edges into bundles to reduce the overall edge crossings. Our method uses a control mesh to guide the edge-clustering process; edge bundles can be formed by forcing all edges to pass through some control points on the mesh. The control mesh can be generated at different levels of detail either manually or automatically based on underlying graph patterns. Users can further interact with the edge-clustering results through several advanced visualization techniques such as color and opacity enhancement. Compared with other edge-clustering methods, our approach is intuitive, flexible, and efficient. The experiments on some large graphs demonstrate the effectiveness of our method.     

SetCoLa: High‐Level Constraints for Graph Layout

Constraints enable flexible graph layout by combining the ease of automatic layout with customizations for a particular domain. However, constraint‐based layout often requires many individual constraints defined over specific nodes and node pairs. In addition to the effort of writing and maintaining a large number of similar constraints, such constraints are specific to the particular graph and thus cannot generalize to other graphs in the same domain. To facilitate the specification of customized and generalizable constraint layouts, we contribute SetCoLa: a domain‐specific language for specifying high‐level constraints relative to properties of the backing data. Users identify node sets based on data or graph properties and apply high‐level constraints within each set. Applying constraints to node sets rather than individual nodes reduces specification effort and facilitates reapplication of customized layouts across distinct graphs. We demonstrate the conciseness, generalizability, and expressiveness of SetCoLa on a series of real‐world examples from ecological networks, biological systems, and social networks.     

The Grasper-CL graph management system

Grasper-CL is a system for manipulating and displaying graphs, and for building graph-based user interfaces for application programs. It is implemented in COMMON LISP and CLIM, and has been proven by use in a number of applications. Grasper-CL includes several advances in graph drawing. It contains a graph abstract datatype plus a comprehensive and novel language of operations on that datatype. The appearance of Grasper-CL graphs can be tailored by a wide variety of shape parameters that allow the application to customize the display of nodes and edges for different domains. Default values for shape parameters can be established at several levels. Grasper-CL employs a toolbox approach to graph layout: the system contains a suite of graph layout algorithms that can be applied individually, or in combination to produce hierarchical graph layouts. The system also contains an interactive graph browser.     

Consumer acceptance of service bundles: An empirical investigation in the context of broadband triple play

Although offering bundled services promises firms potential synergies in supply and increased revenues, the realized benefits of such a strategy are highly contingent on consumer acceptance of the bundles. Borrowing from TAM, Information Integration Theory, and the customer value concept, we developed a comprehensive model for consumer acceptance of service bundles, which is divided into four general construct types: service characteristics, usefulness/ease of use, attitude, and behavioral intention. Twelve hypotheses were derived and empirically tested in the context of broadband triple play, the bundled offering of broadband Internet access, Internet telephony, and Internet TV. Based on questionnaire responses from 214 study participants and using PLS for analysis, we found overall support for our research model. We concluded by discussing the academic and managerial value of our research, both in terms of advanced knowledge of service bundle acceptance and the adoption of triple play.     

Mesh layouts for block-based caches

Current computer architectures employ caching to improve the performance of a wide variety of applications. One of the main characteristics of such cache schemes is the use of block fetching whenever an uncached data element is accessed. To maximize the benefit of the block fetching mechanism, we present novel cache-aware and cache-oblivious layouts of surface and volume meshes that improve the performance of interactive visualization and geometric processing algorithms. Based on a general I/O model, we derive new cache-aware and cache-oblivious metrics that have high correlations with the number of cache misses when accessing a mesh. In addition to guiding the layout process, our metrics can be used to quantify the quality of a layout, e.g. for comparing different layouts of the same mesh and for determining whether a given layout is amenable to significant improvement. We show that layouts of unstructured meshes optimized for our metrics result in improvements over conventional layouts in the performance of visualization applications such as isosurface extraction and view-dependent rendering. Moreover, we improve upon recent cache-oblivious mesh layouts in terms of performance, applicability, and accuracy.