Peacock Bundles: Bundle Coloring for Graphs with Globality-Locality Trade-off

Bundling of graph edges (node-to-node connections) is a common technique to enhance visibility of overall trends in the edge structure of a large graph layout, and a large variety of bundling algorithms have been proposed. However, with strong bundling, it becomes hard to identify origins and destinations of individual edges. We propose a solution: we optimize edge coloring to differentiate bundled edges. We quantify strength of bundling in a flexible pairwise fashion between edges, and among bundled edges, we quantify how dissimilar their colors should be by dissimilarity of their origins and destinations. We solve the resulting nonlinear optimization, which is also interpretable as a novel dimensionality reduction task. In large graphs the necessary compromise is whether to differentiate colors sharply between locally occurring strongly bundled edges ("local bundles"), or also between the weakly bundled edges occurring globally over the graph ("global bundles"); we allow a user-set global-local tradeoff. We call the technique "peacock bundles". Experiments show the coloring clearly enhances comprehensibility of graph layouts with edge bundling.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

Visualizing the dynamics of London's bicycle hire scheme

Visualizing flows between origins and destinations can be straightforward when dealing with small numbers of journeys or simple geographies. Representing flows as lines embedded in geographic space has commonly been used to map transport flows, especially when geographic patterns are important as they are when characterising cities or managing transportation. However, for larger numbers of flows, this approach requires careful design to avoid problems of occlusion, salience bias and information overload. Driven by the requirements identified by users and managers of the London Bicycle Hire scheme we present three methods of representation of bicycle hire use and travel patterns. Flow maps with curved flow symbols are used to show overviews in flow structures. Gridded views of docking station location that preserve geographic relationships are used to explore docking station status over space and time in a graphically efficient manner. Origin-Destination maps that visualise the OD matrix directly while maintaining geographic context are used to provide visual details on demand. We use these approaches to identify changes in travel behaviour over space and time, to aid station rebalancing and to provide a framework for incorporating travel modelling and simulation

Exploring geo-genealogy using internet surname search histories

We present an interactive flow map to visualize aspects of the ways in which surnames have dispersed and migrated around the globe. This work utilizes Internet search queries from the Worldnames Project and uses the density of search locations to determine the node and leaf structures of a flow map. The mapping technique utilized in this work is a variant of geometric minimal Steiner arborescences called the spiral tree. Our implementation is developed in JavaScript to allow for interactive online exploration. Nodes and flow lines can be interactively modified to allow for esthetic changes of color and layout. The results can provide interesting insight into the geography of amateur genealogy

Efficient Generation of Geographically Accurate Transit Maps

We present LOOM (Line-Ordering Optimized Maps), a fully automatic generator of geographically accurate transit maps. The input to LOOM is data about the lines of a given transit network, namely for each line, the sequence of stations it serves and the geographical course the vehicles of this line take. We parse this data from GTFS, the prevailing standard for public transit data. LOOM proceeds in three stages: (1) construct a so-called line graph, where edges correspond to segments of the network with the same set of lines following the same course; (2) construct an ILP that yields a line ordering for each edge which minimizes the total number of line crossings and line separations; (3) based on the line graph and the ILP solution, draw the map. As a naive ILP formulation is too demanding, we derive a new custom-tailored formulation which requires significantly fewer constraints. Furthermore, we present engineering techniques which use structural properties of the line graph to further reduce the ILP size. For the subway network of New York, we can reduce the number of constraints from 229,000 in the naive ILP formulation to about 4,500 with our techniques, enabling solution times of less than a second. Since our maps respect the geography of the transit network, they can be used for tiles and overlays in typical map services. Previous research work either did not take the geographical course of the lines into account, or was concerned with schematic maps without optimizing line crossings or line separations.Comment: 7 page

eXamine: a Cytoscape app for exploring annotated modules in networks

Background. Biological networks have growing importance for the interpretation of high-throughput "omics" data. Statistical and combinatorial methods allow to obtain mechanistic insights through the extraction of smaller subnetwork modules. Further enrichment analyses provide set-based annotations of these modules. Results. We present eXamine, a set-oriented visual analysis approach for annotated modules that displays set membership as contours on top of a node-link layout. Our approach extends upon Self Organizing Maps to simultaneously lay out nodes, links, and set contours. Conclusions. We implemented eXamine as a freely available Cytoscape app. Using eXamine we study a module that is activated by the virally-encoded G-protein coupled receptor US28 and formulate a novel hypothesis about its functioning

A Force-Directed Approach for Offline GPS Trajectory Map Matching

We present a novel algorithm to match GPS trajectories onto maps offline (in batch mode) using techniques borrowed from the field of force-directed graph drawing. We consider a simulated physical system where each GPS trajectory is attracted or repelled by the underlying road network via electrical-like forces. We let the system evolve under the action of these physical forces such that individual trajectories are attracted towards candidate roads to obtain a map matching path. Our approach has several advantages compared to traditional, routing-based, algorithms for map matching, including the ability to account for noise and to avoid large detours due to outliers in the data whilst taking into account the underlying topological restrictions (such as one-way roads). Our empirical evaluation using real GPS traces shows that our method produces better map matching results compared to alternative offline map matching algorithms on average, especially for routes in dense, urban areas.Comment: 10 pages, 12 figures, accepted version of article submitted to ACM SIGSPATIAL 2018, Seattle, US

Improved Optimal and Approximate Power Graph Compression for Clearer Visualisation of Dense Graphs

Drawings of highly connected (dense) graphs can be very difficult to read. Power Graph Analysis offers an alternate way to draw a graph in which sets of nodes with common neighbours are shown grouped into modules. An edge connected to the module then implies a connection to each member of the module. Thus, the entire graph may be represented with much less clutter and without loss of detail. A recent experimental study has shown that such lossless compression of dense graphs makes it easier to follow paths. However, computing optimal power graphs is difficult. In this paper, we show that computing the optimal power-graph with only one module is NP-hard and therefore likely NP-hard in the general case. We give an ILP model for power graph computation and discuss why ILP and CP techniques are poorly suited to the problem. Instead, we are able to find optimal solutions much more quickly using a custom search method. We also show how to restrict this type of search to allow only limited back-tracking to provide a heuristic that has better speed and better results than previously known heuristics.Comment: Extended technical report accompanying the PacificVis 2013 paper of the same nam