Edge Bundles Research Articles

The Case for Optimized Edge-Centric Tractography at Scale.

The anatomic validity of structural connectomes remains a significant uncertainty in neuroimaging. Edge-centric tractography reconstructs streamlines in bundles between each pair of cortical or subcortical regions. Although edge bundles provides a stronger anatomic embedding than traditional connectomes, calculating them for each region-pair requires exponentially greater computation. We observe that major speedup can be achieved by reducing the number of streamlines used by probabilistic tractography algorithms. To ensure this does not degrade connectome quality, we calculate the identifiability of edge-centric connectomes between test and re-test sessions as a proxy for information content. We find that running PROBTRACKX2 with as few as 1 streamline per voxel per region-pair has no significant impact on identifiability. Variation in identifiability caused by streamline count is overshadowed by variation due to subject demographics. This finding even holds true in an entirely different tractography algorithm using MRTrix. Incidentally, we observe that Jaccard similarity is more effective than Pearson correlation in calculating identifiability for our subject population.

Multigroup connectivity structures and their implications

AbstractWe investigate the implications of different forms of multigroup connectivity. Four multigroup connectivity modalities are considered: co-memberships, edge bundles, bridges, and liaison hierarchies. We propose generative models to generate these four modalities. Our models are variants of planted partition or stochastic block models conditioned under certain topological constraints. We report findings of a comparative analysis in which we evaluate these structures, controlling for their edge densities and sizes, on mean rates of information propagation, convergence times to consensus, and steady-state deviations from the consensus value in the presence of noise as network size increases.

The Effect of Edge Bundling and Seriation on Sensemaking of Biclusters in Bipartite Graphs.

Exploring coordinated relationships (e.g., shared relationships between two sets of entities) is an important analytics task in a variety of real-world applications, such as discovering similarly behaved genes in bioinformatics, detecting malware collusions in cyber security, and identifying products bundles in marketing analysis. Coordinated relationships can be formalized as biclusters. In order to support visual exploration of biclusters, bipartite graphs based visualizations have been proposed, and edge bundling is used to show biclusters. However, it suffers from edge crossings due to possible overlaps of biclusters, and lacks in-depth understanding of its impact on user exploring biclusters in bipartite graphs. To address these, we propose a novel bicluster-based seriation technique that can reduce edge crossings in bipartite graphs drawing and conducted a user experiment to study the effect of edge bundling and this proposed technique on visualizing biclusters in bipartite graphs. We found that they both had impact on reducing entity visits for users exploring biclusters, and edge bundles helped them find more justified answers. Moreover, we identified four key trade-offs that inform the design of future bicluster visualizations. The study results suggest that edge bundling is critical for exploring biclusters in bipartite graphs, which helps to reduce low-level perceptual problems and support high-level inferences.

Hierarchical sets: analyzing pangenome structure through scalable set visualizations.

MotivationThe increase in available microbial genome sequences has resulted in an increase in the size of the pangenomes being analyzed. Current pangenome visualizations are not intended for the pangenome sizes possible today and new approaches are necessary in order to convert the increase in available information to increase in knowledge. As the pangenome data structure is essentially a collection of sets we explore the potential for scalable set visualization as a tool for pangenome analysis.ResultsWe present a new hierarchical clustering algorithm based on set arithmetics that optimizes the intersection sizes along the branches. The intersection and union sizes along the hierarchy are visualized using a composite dendrogram and icicle plot, which, in pangenome context, shows the evolution of pangenome and core size along the evolutionary hierarchy. Outlying elements, i.e. elements whose presence pattern do not correspond with the hierarchy, can be visualized using hierarchical edge bundles. When applied to pangenome data this plot shows putative horizontal gene transfers between the genomes and can highlight relationships between genomes that is not represented by the hierarchy. We illustrate the utility of hierarchical sets by applying it to a pangenome based on 113 Escherichia and Shigella genomes and find it provides a powerful addition to pangenome analysis.Availability and ImplementationThe described clustering algorithm and visualizations are implemented in the hierarchicalSets R package available from CRAN (https://cran.r-project.org/web/packages/hierarchicalSets)Supplementary information Supplementary data are available at Bioinformatics online.

BiSet: Semantic Edge Bundling with Biclusters for Sensemaking.

Identifying coordinated relationships is an important task in data analytics. For example, an intelligence analyst might want to discover three suspicious people who all visited the same four cities. Existing techniques that display individual relationships, such as between lists of entities, require repetitious manual selection and significant mental aggregation in cluttered visualizations to find coordinated relationships. In this paper, we present BiSet, a visual analytics technique to support interactive exploration of coordinated relationships. In BiSet, we model coordinated relationships as biclusters and algorithmically mine them from a dataset. Then, we visualize the biclusters in context as bundled edges between sets of related entities. Thus, bundles enable analysts to infer task-oriented semantic insights about potentially coordinated activities. We make bundles as first class objects and add a new layer, "in-between", to contain these bundle objects. Based on this, bundles serve to organize entities represented in lists and visually reveal their membership. Users can interact with edge bundles to organize related entities, and vice versa, for sensemaking purposes. With a usage scenario, we demonstrate how BiSet supports the exploration of coordinated relationships in text analytics.

Bundled Visualization of DynamicGraph and Trail Data.

Depicting change captured by dynamic graphs and temporal paths, or trails, is hard. We present two techniques for simplified visualization of such data sets using edge bundles. The first technique uses an efficient image-based bundling method to create smoothly changing bundles from streaming graphs. The second technique adds edge-correspondence data atop of any static bundling algorithm, and is best suited for graph sequences. We show how these techniques can produce simplified visualizations of streaming and sequence graphs. Next, we show how several temporal attributes can be added atop of our dynamic graphs. We illustrate our techniques with data sets from aircraft monitoring, software engineering, and eye-tracking of static and dynamic scenes.

Image‐Based Edge Bundles: Simplified Visualization of Large Graphs

AbstractWe 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.

Smooth Graphs for Visual Exploration of Higher-Order State Transitions

In this paper, we present a new visual way of exploring state sequences in large observational time-series. A key advantage of our method is that it can directly visualize higher-order state transitions. A standard first order state transition is a sequence of two states that are linked by a transition. A higher-order state transition is a sequence of three or more states where the sequence of participating states are linked together by consecutive first order state transitions. Our method extends the current state-graph exploration methods by employing a two dimensional graph, in which higher-order state transitions are visualized as curved lines. All transitions are bundled into thick splines, so that the thickness of an edge represents the frequency of instances. The bundling between two states takes into account the state transitions before and after the transition. This is done in such a way that it forms a continuous representation in which any subsequence of the time series is represented by a continuous smooth line. The edge bundles in these graphs can be explored interactively through our incremental selection algorithm.We demonstrate our method with an application in exploring labeled time-series data from a biological survey, where a clustering has assigned a single label to the data at each time-point. In these sequences, a large number of cyclic patterns occur, which in turn are linked to specific activities. We demonstrate how our method helps to find these cycles, and how the interactive selection process helps to find and investigate activities.

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.

Visual Comparison of Hierarchically Organized Data

AbstractWe provide a novel visualization method for the comparison of hierarchically organized data. Our technique visualizes a pair of hierarchies that are to be compared and simultaneously depicts how these hierarchies are related by explicitly visualizing the relations between matching subhierarchies. Elements that are unique to each hierarchy are shown, as well as the way in which hierarchy elements are relocated, split or joined. The relations between hierarchy elements are visualized using Hierarchical Edge Bundles (HEBs). HEBs reduce visual clutter, they visually emphasize the aforementioned splits, joins, and relocations of subhierarchies, and they provide an intuitive way in which users can interact with the relations. The focus throughout this paper is on the comparison of different versions of hierarchically organized software systems, but the technique is applicable to other kinds of hierarchical data as well. Various data sets of actual software systems are used to show how our technique can be employed to easily spot splits, joins, and relocations of elements, how sorting both hierarchies with respect to each other facilitates comparison tasks, and how user interaction is supported.

Formation and stability of saturated bundled structure (SBS) in Ti 3Al single crystals cyclically deformed by double prism slip

Formation and stability of deformation substructure in fatigued Ti 3Al single crystals deformed by double prism slip were examined under different applied strain amplitude ( Δ ε). The specimens were initially fatigued at Δ ε=±0.2% or ±0.3% for 1×10 4 cycles and subsequently cyclically deformed after the change in Δ ε from ±0.2% to ±0.3% or from ±0.3% to ±0.2%. The saturated bundled structure (SBS) was composed of the bundles with high density of edge dislocations aligning along [0001] and screw dislocations between the bundles were formed in specimens fatigued at initial Δ ε to the saturated stage. The bundles in the SBS were developed and expanded after the increase in Δ ε to ±0.3%, while the rearrangement of screw dislocations occurred and some parts of the saturated edge bundles were removed after the decrease in Δ ε to ±0.2%. The thermal stability of the fatigued substructure was examined in order to understand the formation process of edge dipoles and debris in the SBS. The change in the maximum shear stress amplitude and the Bauschinger effect were also examined during cyclic deformation.