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.     

An Example‐based Approach to Synthesize Artistic Strokes using Graphs

In this paper, we propose a technique to produce artistic strokes in a variety of drawing material based on example images. Our approach is to divide example strokes scanned from images into small pieces along their stroke directions and synthesize a novel stroke by rearranging them along a user specified curve. The visible quality of a synthesized stroke can be maintained by utilizing the connectivity information stored in a directed graph constructed in the preprocessing step. At run‐time, the graph is traversed to find a path best matching the user specification given as a curve and additional information. The results of our experiments shows that visually convincing strokes of various materials can be generated efficiently.     

Metro Transit‐Centric Visualization for City Tour Planning

In general, city trip planning consists of two main steps: knowing Points‐Of‐Interest (POIs), and then planning a tour route from the current point to next preferred POIs. We mainly consider the metro for traveling around touristic cities as the main means of transportation. In this context, existing tools lack a capability to effectively visualize POIs on the metro map for trip planning. To bridge this gap, we propose an interactive framework that holistically combines presentations of POIs and a metro network. Our idea is to identify popular POIs based on visual worth computation, and to introduce POI discovery for effectively identifying POIs within reach of a metro network for users. We use octilinear layouts to highlight the metro network, and show representative POI images in the layout space visualized within a user‐specified viewing window. We have implemented our working prototype showing touristic cities with a metro network. We have factored out various design guidelines that are basis for designing our method, and validated our approach with a user study surveying 70 individuals.     

Interactive Reconfiguration of Urban Layouts

The layout of an urban space is a complex collection of man-made structures arranged in parcels, city blocks, and neighborhoods. An editor for interactively reconfiguring city layouts exploits geographical information system (GIS) data and provides tools to expand, scale, replace, and move parcels and blocks while efficiently exploiting their connectivity and zoning. The ability to create, extend, and change a model of a large-scale urban environment is useful for a variety of computer graphics applications. For example, it lets urban planning applications simulate changes to city layouts or newly proposed neighborhoods, create hypothetical views of an urban area after applying development and growth algorithms, and show architects the results of using common building blocks to design a new city layout.     

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.     

Techniques for Edge Stratification of Complex Graph Drawings

We propose an approach that allows a user (e.g., an analyst) to explore a layout produced by any graph drawing algorithm, in order to reduce the visual complexity and clarify its presentation. Our approach is based on stratifying the drawing into layers with desired properties; to this aim, heuristics are presented. The produced layers can be explored and combined by the user to gradually acquire details. We present a user study to test the effectiveness of our approach. Furthermore, we performed an experimental analysis on popular force-directed graph drawing algorithms, in order to evaluate what is the algorithm that produces the smallest number of layers and if there is any correlation between the number of crossings and the number of layers of a graph layout. The proposed approach is useful to explore graph layouts, as confirmed by the presented user study. Furthermore, interesting considerations arise from the experimental evaluation, in particular, our results suggest that the number of layers of a graph layout may represent a reliable measure of its visual complexity. The algorithms presented in this paper can be effectively applied to graph layouts with a few hundreds of edges and vertices. For larger drawings that contain lots of crossings, the time complexity of our algorithms grows quadratically in the number of edges and more efficient techniques need to be devised. The proposed approach takes as input a layout produced by any graph drawing algorithm, therefore it can be applied in a variety of application domains. Several research directions can be explored to extend our framework and to devise new visualization paradigms to effectively present stratified drawings.     

Exact solution for the optimal neuronal layout problem

Evolution perfected brain design by maximizing its functionality while minimizing costs associated with building and maintaining it. Assumption that brain functionality is specified by neuronal connectivity, implemented by costly biological wiring, leads to the following optimal design problem. For a given neuronal connectivity, find a spatial layout of neurons that minimizes the wiring cost. Unfortunately, this problem is difficult to solve because the number of possible layouts is often astronomically large. We argue that the wiring cost may scale as wire length squared, reducing the optimal layout problem to a constrained minimization of a quadratic form. For biologically plausible constraints, this problem has exact analytical solutions, which give reasonable approximations to actual layouts in the brain. These solutions make the inverse problem of inferring neuronal connectivity from neuronal layout more tractable.     

Procedural Arrangement of Furniture for Real‐Time Walkthroughs

This paper presents a procedural approach to generate furniture arrangements for large virtual indoor scenes. The interiors of buildings in 3D city scenes are often omitted. Our solution creates rich furniture arrangements for all rooms of complex buildings and even for entire cities. The key idea is to only furnish the rooms in the vicinity of the viewer while the user explores a building in real time. In order to compute the object layout we introduce an agent‐based solution and demonstrate the flexibility and effectiveness of the agent approach. Furthermore, we describe advanced features of the system, like procedural furniture geometry, persistent room layouts, and styles for high‐level control.     

MIQP‐based Layout Design for Building Interiors

We propose a hierarchical framework for the generation of building interiors. Our solution is based on a mixed integer quadratic programming (MIQP) formulation. We parametrize a layout by polygons that are further decomposed into small rectangles. We identify important high‐level constraints, such as room size, room position, room adjacency, and the outline of the building, and formulate them in a way that is compatible with MIQP and the problem parametrization. We also propose a hierarchical framework to improve the scalability of the approach. We demonstrate that our algorithm can be used for residential building layouts and can be scaled up to large layouts such as office buildings, shopping malls, and supermarkets. We show that our method is faster by multiple orders of magnitude than previous methods.     

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.     

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.     

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.     

Perfect Matching Quad Layouts for Manifold Meshes

This paper introduces a new approach to automatically generate pure quadrilateral patch layouts on manifold meshes. The algorithm is based on a careful construction of a singularity graph of a given input frame field or a given periodic global parameterization. A pure quadrilateral patch layout is then derived as a constrained minimum weight perfect matching of that graph. The resulting layout is optimal relative to a balance between coarseness and geometric feature alignment. We formulate the problem of finding pure quadrilateral patch layouts as a global optimization problem related to a well‐known concept in graph theory. The main advantage of the new method is its simplicity and its computation speed. Patch layouts generated by the present algorithm are high quality and are very competitive compared to current state of the art.     

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.     

A Comparison of User-Generated and Automatic Graph Layouts

The research presented in this paper compares user-generated and automatic graph layouts. Following the methods suggested by van Ham et al. (2008), a group of users generated graph layouts using both multi-touch interaction on a tabletop display and mouse interaction on a desktop computer. Users were asked to optimize their layout for aesthetics and analytical tasks with a social network. We discuss characteristics of the user-generated layouts and interaction methods employed by users in this process. We then report on a web-based study to compare these layouts with the output of popular automatic layout algorithms. Our results demonstrate that the best of the user-generated layouts performed as well as or better than the physics-based layout. Orthogonal and circular automatic layouts were found to be considerably less effective than either the physics-based layout or the best of the user-generated layouts. We highlight several attributes of the various layouts that led to high accuracy and improved task completion time, as well as aspects in which traditional automatic layout methods were unsuccessful for our tasks.     

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.     

Fast Feature‐Oriented Visual Connection for Large Image Collections

Deriving the visual connectivity across large image collections is a computationally expensive task. Different from current image‐oriented match graph construction methods which build on pairwise image matching, we present a novel and scalable feature‐oriented image matching algorithm for large collections. Our method improves the match graph construction procedure in three ways. First, instead of building trees repeatedly, we put the feature points of the input image collection into a single kd‐tree and select the leaves as our anchor points. Then we construct an anchor graph from which each feature can intelligently find a small portion of related candidates to match. Finally, we design a new form of adjacency matrix for fast feature similarity measuring, and return all the matches in different photos across the whole dataset directly. Experiments show that our feature‐oriented correspondence algorithm can explore visual connectivity between images with significant improvement in speed.     

An Example-based Procedural System for Element Arrangement

We present a method for synthesizing two dimensional (2D) element arrangements from an example. The main idea is to combine texture synthesis techniques based‐on a local neighborhood comparison and procedural modeling systems based‐on local growth. Given a user‐specified reference pattern, our system analyzes neigh‐borhood information of each element by constructing connectivity. Our synthesis process starts with a single seed and progressively places elements one by one by searching a reference element which has local features that are the most similar to the target place of the synthesized pattern. To support creative design activities, we introduce three types of interaction for controlling global features of the resulting pattern, namely a spray tool, a flow field tool, and a boundary tool. We also introduce a global optimization process that helps to avoid local error concentrations. We illustrate the feasibility of our method by creating several types of 2D patterns.     

Newspaper article reconstruction using ant colony optimization and bipartite graph

The primary information units in a newspaper are the articles. How to segment a newspaper page into individual articles and to recover the reading order of each article, namely newspaper article reconstruction, is known to be challenging due to the complexity of the multi-article page layout. In this paper, we propose a novel article reconstruction approach by solving a series of subtasks: grouping the article bodies, detecting the reading order, associating the title-body pairs and linking article parts scattered in multiple pages. We formulate reading order detection as a traveling salesman problem (TSP), and employ the Max-Min Ant System (MMAS) to solve it. Furthermore, a level-based pheromone mechanism is introduced to improve the efficiency of standard MMAS. Moreover, in sharp contrast to the existing methods, we perform the first two subtasks of article reconstruction in reverse order, that is, we detect the reading order of the text blocks first and then use the content continuity implicitly specified in the reading order to aggregate text blocks of the same article. In this way, we can effectively overcome the limitation of content similarity on article body aggregation. The other two subtasks (associating the title-body pairs, linking article parts scattered in multiple pages), are solved under a unified bipartite graph framework, which models the complex relationships between page objects as one-to-one correspondences, and accomplishes the two subtasks by finding the optimal matching on this graph. During the optimization process, various information sources, including geometric layout, linguistic and semantic content, are deeply mined in MMAS and bipartite graph model to deal with the wide range of complex newspaper layouts. Experimental results on real-world data have demonstrated the effectiveness of our proposed method. It has also been adopted in several large-scale newspaper digitalization projects.