AmbiguityVis: Visualization of Ambiguity in Graph Layouts

Graph Exploration With Embedding-Guided Layouts

Node-link diagrams are widely used to visualize graphs. Most graph layout algorithms only use graph topology for aesthetic goals (e.g., minimize node occlusions and edge crossings) or use node attributes for exploration goals (e.g., preserve visible communities). Existing hybrid methods that bind the two perspectives still suffer from various generation restrictions (e.g., limited input types and required manual adjustments and prior knowledge of graphs) and the imbalance between aesthetic and exploration goals. In this article, we propose a flexible embedding-based graph exploration pipeline to enjoy the best of both graph topology and node attributes. First, we leverage embedding algorithms for attributed graphs to encode the two perspectives into latent space. Then, we present an embedding-driven graph layout algorithm, GEGraph, which can achieve aesthetic layouts with better community preservation to support an easy interpretation of the graph structure. Next, graph explorations are extended based on the generated graph layout and insights extracted from the embedding vectors. Illustrated with examples, we build a layout-preserving aggregation method with Focus+Context interaction and a related nodes searching approach with multiple proximity strategies. Finally, we conduct quantitative and qualitative evaluations, a user study, and two case studies to validate our approach.

Evaluating Effects of Background Stories on Graph Perception

A graph is an abstract model that represents relations among entities, for example, the interactions between characters in a novel. A background story endows entities and relations with real-world meanings and describes the semantics and context of the abstract model, for example, the actual story that the novel presents. Considering practical experience and prior research, human viewers who are familiar with the background story of a graph and those who do not know the background story may perceive the same graph differently. However, no previous research has adequately addressed this problem. This research article thus presents an evaluation that investigated the effects of background stories on graph perception. Three hypotheses that focused on the role of visual focus areas, graph structure identification, and mental model formation on graph perception were formulated and guided three controlled experiments that evaluated the hypotheses using real-world graphs with background stories. An analysis of the resulting experimental data, which compared the performance of participants who read and did not read the background stories, obtained a set of instructive findings. First, having knowledge about a graph's background story influences participants' focus areas during interactive graph explorations. Second, such knowledge significantly affects one's ability to identify community structures but not high degree and bridge structures. Third, this knowledge influences graph recognition under blurred visual conditions. These findings can bring new considerations to the design of storytelling visualizations and interactive graph explorations.

Edge-Path Bundling: A Less Ambiguous Edge Bundling Approach

Edge bundling techniques cluster edges with similar attributes (i.e. similarity in direction and proximity) together to reduce the visual clutter. All edge bundling techniques to date implicitly or explicitly cluster groups of individual edges, or parts of them, together based on these attributes. These clusters can result in ambiguous connections that do not exist in the data. Confluent drawings of networks do not have these ambiguities, but require the layout to be computed as part of the bundling process. We devise a new bundling method, Edge-Path bundling, to simplify edge clutter while greatly reducing ambiguities compared to previous bundling techniques. Edge-Path bundling takes a layout as input and clusters each edge along a weighted, shortest path to limit its deviation from a straight line. Edge-Path bundling does not incur independent edge ambiguities typically seen in all edge bundling methods, and the level of bundling can be tuned through shortest path distances, Euclidean distances, and combinations of the two. Also, directed edge bundling naturally emerges from the model. Through metric evaluations, we demonstrate the advantages of Edge-Path bundling over other techniques.

Visualizing Uncertainty in Probabilistic Graphs with Network Hypothetical Outcome Plots (NetHOPs)

Probabilistic graphs are challenging to visualize using the traditional node-link diagram. Encoding edge probability using visual variables like width or fuzziness makes it difficult for users of static network visualizations to estimate network statistics like densities, isolates, path lengths, or clustering under uncertainty. We introduce Network Hypothetical Outcome Plots (NetHOPs), a visualization technique that animates a sequence of network realizations sampled from a network distribution defined by probabilistic edges. NetHOPs employ an aggregation and anchoring algorithm used in dynamic and longitudinal graph drawing to parameterize layout stability for uncertainty estimation. We present a community matching algorithm to enable visualizing the uncertainty of cluster membership and community occurrence. We describe the results of a study in which 51 network experts used NetHOPs to complete a set of common visual analysis tasks and reported how they perceived network structures and properties subject to uncertainty. Participants' estimates fell, on average, within 11% of the ground truth statistics, suggesting NetHOPs can be a reasonable approach for enabling network analysts to reason about multiple properties under uncertainty. Participants appeared to articulate the distribution of network statistics slightly more accurately when they could manipulate the layout anchoring and the animation speed. Based on these findings, we synthesize design recommendations for developing and using animated visualizations for probabilistic networks.

A Visual Analytics Approach for Exploratory Causal Analysis: Exploration, Validation, and Applications

Using causal relations to guide decision making has become an essential analytical task across various domains, from marketing and medicine to education and social science. While powerful statistical models have been developed for inferring causal relations from data, domain practitioners still lack effective visual interface for interpreting the causal relations and applying them in their decision-making process. Through interview studies with domain experts, we characterize their current decision-making workflows, challenges, and needs. Through an iterative design process, we developed a visualization tool that allows analysts to explore, validate, and apply causal relations in real-world decision-making scenarios. The tool provides an uncertainty-aware causal graph visualization for presenting a large set of causal relations inferred from high-dimensional data. On top of the causal graph, it supports a set of intuitive user controls for performing what-if analyses and making action plans. We report on two case studies in marketing and student advising to demonstrate that users can effectively explore causal relations and design action plans for reaching their goals.

Context-aware Sampling of Large Networks via Graph Representation Learning

Numerous sampling strategies have been proposed to simplify large-scale networks for highly readable visualizations. It is of great challenge to preserve contextual structures formed by nodes and edges with tight relationships in a sampled graph, because they are easily overlooked during the process of sampling due to their irregular distribution and immunity to scale. In this paper, a new graph sampling method is proposed oriented to the preservation of contextual structures. We first utilize a graph representation learning (GRL) model to transform nodes into vectors so that the contextual structures in a network can be effectively extracted and organized. Then, we propose a multi-objective blue noise sampling model to select a subset of nodes in the vectorized space to preserve contextual structures with the retention of relative data and cluster densities in addition to those features of significance, such as bridging nodes and graph connections. We also design a set of visual interfaces enabling users to interactively conduct context-aware sampling, visually compare results with various sampling strategies, and deeply explore large networks. Case studies and quantitative comparisons based on real-world datasets have demonstrated the effectiveness of our method in the abstraction and exploration of large networks.

Analyzing Dynamic Hypergraphs with Parallel Aggregated Ordered Hypergraph Visualization

Parallel Aggregated Ordered Hypergraph(PAOH) is a novel technique to visualize dynamic hypergraphs. Hypergraphs are a generalization of graphs where edges can connect several vertices. Hypergraphs can be used to model networks of business partners or co-authorship networks with multiple authors per article. A dynamic hypergraph evolves over discrete time slots. PAOH represents vertices as parallel horizontal bars and hyperedges as vertical lines, using dots to depict the connections to one or more vertices. We describe a prototype implementation of Parallel Aggregated Ordered Hypergraph, report on a usability study with 9 participants analyzing publication data, and summarize the improvements made. Two case studies and several examples are provided. We believe that PAOH is the first technique to provide a highly readable representation of dynamic hypergraphs. It is easy to learn and well suited for medium size dynamic hypergraphs (50-500 vertices) such as those commonly generated by digital humanities projects-our driving application domain.

Visual Quality Guidance for Document Exploration with Focus+Context Techniques

Magic lens based focus+context techniques are powerful means for exploring document spatializations. Typically, they only offer additional summarized or abstracted views on focused documents. As a consequence, users might miss important information that is either not shown in aggregated form or that never happens to get focused. In this work, we present the design process and user study results for improving a magic lens based document exploration approach with exemplary visual quality cues to guide users in steering the exploration and support them in interpreting the summarization results. We contribute a thorough analysis of potential sources of information loss involved in these techniques, which include the visual spatialization of text documents, user-steered exploration, and the visual summarization. With lessons learned from previous research, we highlight the various ways those information losses could hamper the exploration. Furthermore, we formally define measures for the aforementioned different types of information losses and bias. Finally, we present the visual cues to depict these quality measures that are seamlessly integrated into the exploration approach. These visual cues guide users during the exploration and reduce the risk of misinterpretation and accelerate insight generation. We conclude with the results of a controlled user study and discuss the benefits and challenges of integrating quality guidance in exploration techniques.

The Sprawlter Graph Readability Metric: Combining Sprawl and Area-Aware Clutter

Graph drawing readability metrics are routinely used to assess and create node-link layouts of network data. Existing readability metrics fall short in three ways. The many count-based metrics such as edge-edge or node-edge crossings simply provide integer counts, missing the opportunity to quantify the amount of overlap between items, which may vary in size, at a more fine-grained level. Current metrics focus solely on single-level topological structure, ignoring the possibility of multi-level structure such as large and thus highly salient metanodes. Most current metrics focus on the measurement of clutter in the form of crossings and overlaps, and do not take into account the trade-off between the clutter and the information sparsity of the drawing, which we refer to as sprawl. We propose an area-aware approach to clutter metrics that tracks the extent of geometric overlaps between node-node, node-edge, and edge-edge pairs in detail. It handles variable-size nodes and explicitly treats metanodes and leaf nodes uniformly. We call the combination of a sprawl metric and an area-aware clutter metric a sprawlter metric. We present an instantiation of the sprawlter metrics featuring a formal and thorough discussion of the crucial component, the penalty mapping function. We implement and validate our proposed metrics with extensive computational analysis of graph layouts, considering four layout algorithms and 56 layouts encompassing both real-world data and synthetic examples illustrating specific configurations of interest.

Interactive Structure-aware Blending of Diverse Edge Bundling Visualizations

Many edge bundling techniques (i.e., data simplification as a support for data visualization and decision making) exist but they are not directly applicable to any kind of dataset and their parameters are often too abstract and difficult to set up. As a result, this hinders the user ability to create efficient aggregated visualizations. To address these issues, we investigated a novel way of handling visual aggregation with a task-driven and user-centered approach. Given a graph, our approach produces a decluttered view as follows: first, the user investigates different edge bundling results and specifies areas, where certain edge bundling techniques would provide user-desired results. Second, our system then computes a smooth and structural preserving transition between these specified areas. Lastly, the user can further fine-tune the global visualization with a direct manipulation technique to remove the local ambiguity and to apply different visual deformations. In this paper, we provide details for our design rationale and implementation. Also, we show how our algorithm gives more suitable results compared to current edge bundling techniques, and in the end, we provide concrete instances of usages, where the algorithm combines various edge bundling results to support diverse data exploration and visualizations.

OD Morphing: Balancing Simplicity with Faithfulness for OD Bundling

OD bundling is a promising method to identify key origin-destination (OD) patterns, but the bundling can mislead the interpretation of actual trajectories traveled. We present OD Morphing, an interactive OD bundling technique that improves geographical faithfulness to actual trajectories while preserving visual simplicity for OD patterns. OD Morphing iteratively identifies critical waypoints from the actual trajectory network with a min-cut algorithm and transitions OD bundles to pass through the identified waypoints with a smooth morphing method. Furthermore, we extend OD Morphing to support bundling at interaction speeds to enable users to interactively transition between degrees of faithfulness to aid sensemaking. We introduce metrics for faithfulness and simplicity to evaluate their trade-off achieved by OD morphed bundling. We demonstrate OD Morphing on real-world city-scale taxi trajectory and USA domestic planned flight datasets.

DeepDrawing: A Deep Learning Approach to Graph Drawing

Node-link diagrams are widely used to facilitate network explorations. However, when using a graph drawing technique to visualize networks, users often need to tune different algorithm-specific parameters iteratively by comparing the corresponding drawing results in order to achieve a desired visual effect. This trial and error process is often tedious and time-consuming, especially for non-expert users. Inspired by the powerful data modelling and prediction capabilities of deep learning techniques, we explore the possibility of applying deep learning techniques to graph drawing. Specifically, we propose using a graph-LSTM-based approach to directly map network structures to graph drawings. Given a set of layout examples as the training dataset, we train the proposed graph-LSTM-based model to capture their layout characteristics. Then, the trained model is used to generate graph drawings in a similar style for new networks. We evaluated the proposed approach on two special types of layouts (i.e., grid layouts and star layouts) and two general types of layouts (i.e., ForceAtlas2 and PivotMDS) in both qualitative and quantitative ways. The results provide support for the effectiveness of our approach. We also conducted a time cost assessment on the drawings of small graphs with 20 to 50 nodes. We further report the lessons we learned and discuss the limitations and future work.

Evaluating the Readability of Force Directed Graph Layouts: A Deep Learning Approach

Existing graph layout algorithms are usually not able to optimize all the aesthetic properties desired in a graph layout. To evaluate how well the desired visual features are reflected in a graph layout, many readability metrics have been proposed in the past decades. However, the calculation of these readability metrics often requires access to the node and edge coordinates and is usually computationally inefficient, especially for dense graphs. Importantly, when the node and edge coordinates are not accessible, it becomes impossible to evaluate the graph layouts quantitatively. In this paper, we present a novel deep learning-based approach to evaluate the readability of graph layouts by directly using graph images. A convolutional neural network architecture is proposed and trained on a benchmark dataset of graph images, which is composed of synthetically generated graphs and graphs created by sampling from real large networks. Multiple representative readability metrics (including edge crossing, node spread, and group overlap) are considered in the proposed approach. We quantitatively compare our approach to traditional methods and qualitatively evaluate our approach by showing usage scenarios and visualizing convolutional layers. This paper is a first step towards using deep learning based methods to quantitatively evaluate images from the visualization field.

An Information-Theoretic Framework for Evaluating Edge Bundling Visualization

Edge bundling is a promising graph visualization approach to simplifying the visual result of a graph drawing. Plenty of edge bundling methods have been developed to generate diverse graph layouts. However, it is difficult to defend an edge bundling method with its resulting layout against other edge bundling methods as a clear theoretic evaluation framework is absent in the literature. In this paper, we propose an information-theoretic framework to evaluate the visual results of edge bundling techniques. We first illustrate the advantage of edge bundling visualizations for large graphs, and pinpoint the ambiguity resulting from drawing results. Second, we define and quantify the amount of information delivered by edge bundling visualization from the underlying network using information theory. Third, we propose a new algorithm to evaluate the resulting layouts of edge bundling using the amount of the mutual information between a raw network dataset and its edge bundling visualization. Comparison examples based on the proposed framework between different edge bundling techniques are presented.

Visual Abstraction of Large Scale Geospatial Origin-Destination Movement Data

A variety of human movement datasets are represented in an Origin-Destination(OD) form, such as taxi trips, mobile phone locations, etc. As a commonly-used method to visualize OD data, flow map always fails to discover patterns of human mobility, due to massive intersections and occlusions of lines on a 2D geographical map. A large number of techniques have been proposed to reduce visual clutter of flow maps, such as filtering, clustering and edge bundling, but the correlations of OD flows are often neglected, which makes the simplified OD flow map present little semantic information. In this paper, a characterization of OD flows is established based on an analogy between OD flows and natural language processing (NPL) terms. Then, an iterative multi-objective sampling scheme is designed to select OD flows in a vectorized representation space. To enhance the readability of sampled OD flows, a set of meaningful visual encodings are designed to present the interactions of OD flows. We design and implement a visual exploration system that supports visual inspection and quantitative evaluation from a variety of perspectives. Case studies based on real-world datasets and interviews with domain experts have demonstrated the effectiveness of our system in reducing the visual clutter and enhancing correlations of OD flows.

A taxonomy of visualization tasks for the analysis of biological pathway data

BACKGROUND

Understanding complicated networks of interactions and chemical components is essential to solving contemporary problems in modern biology, especially in domains such as cancer and systems research. In these domains, biological pathway data is used to represent chains of interactions that occur within a given biological process. Visual representations can help researchers understand, interact with, and reason about these complex pathways in a number of ways. At the same time, these datasets offer unique challenges for visualization, due to their complexity and heterogeneity.

RESULTS

Here, we present taxonomy of tasks that are regularly performed by researchers who work with biological pathway data. The generation of these tasks was done in conjunction with interviews with several domain experts in biology. These tasks require further classification than is provided by existing taxonomies. We also examine existing visualization techniques that support each task, and we discuss gaps in the existing visualization space revealed by our taxonomy.

CONCLUSIONS

Our taxonomy is designed to support the development and design of future biological pathway visualization applications. We conclude by suggesting future research directions based on our taxonomy and motivated by the comments received by our domain experts.

Probabilistic Graph Layout for Uncertain Network Visualization

We present a novel uncertain network visualization technique based on node-link diagrams. Nodes expand spatially in our probabilistic graph layout, depending on the underlying probability distributions of edges. The visualization is created by computing a two-dimensional graph embedding that combines samples from the probabilistic graph. A Monte Carlo process is used to decompose a probabilistic graph into its possible instances and to continue with our graph layout technique. Splatting and edge bundling are used to visualize point clouds and network topology. The results provide insights into probability distributions for the entire network-not only for individual nodes and edges. We validate our approach using three data sets that represent a wide range of network types: synthetic data, protein-protein interactions from the STRING database, and travel times extracted from Google Maps. Our approach reveals general limitations of the force-directed layout and allows the user to recognize that some nodes of the graph are at a specific position just by chance.

Characterizing Guidance in Visual Analytics

Visual analytics (VA) is typically applied in scenarios where complex data has to be analyzed. Unfortunately, there is a natural correlation between the complexity of the data and the complexity of the tools to study them. An adverse effect of complicated tools is that analytical goals are more difficult to reach. Therefore, it makes sense to consider methods that guide or assist users in the visual analysis process. Several such methods already exist in the literature, yet we are lacking a general model that facilitates in-depth reasoning about guidance. We establish such a model by extending van Wijk's model of visualization with the fundamental components of guidance. Guidance is defined as a process that gradually narrows the gap that hinders effective continuation of the data analysis. We describe diverse inputs based on which guidance can be generated and discuss different degrees of guidance and means to incorporate guidance into VA tools. We use existing guidance approaches from the literature to illustrate the various aspects of our model. As a conclusion, we identify research challenges and suggest directions for future studies. With our work we take a necessary step to pave the way to a systematic development of guidance techniques that effectively support users in the context of VA.

Typology of Uncertainty in Static Geolocated Graphs for Visualization

Static geolocated graphs have nodes connected by edges, where both can have geographic location and associated attributes. For example, it can be uncertain exactly where a node is located or whether an edge between two nodes exists. Because source data is often incomplete or inexact, it is necessary to visualize this uncertainty to help users make appropriate decisions. The proposed typology of uncertainty extends related typologies with specific features needed for characterizing uncertainty in static geolocated graphs.