Persistent Homology Guided Force-Directed Graph Layouts

Graphs are commonly used to encode relationships among entities, yet their abstractness makes them difficult to analyze. Node-link diagrams are popular for drawing graphs, and force-directed layouts provide a flexible method for node arrangements that use local relationships in an attempt to reveal the global shape of the graph. However, clutter and overlap of unrelated structures can lead to confusing graph visualizations. This paper leverages the persistent homology features of an undirected graph as derived information for interactive manipulation of force-directed layouts. We first discuss how to efficiently extract 0-dimensional persistent homology features from both weighted and unweighted undirected graphs. We then introduce the interactive persistence barcode used to manipulate the force-directed graph layout. In particular, the user adds and removes contracting and repulsing forces generated by the persistent homology features, eventually selecting the set of persistent homology features that most improve the layout. Finally, we demonstrate the utility of our approach across a variety of synthetic and real datasets

Xpertum

Improve the innovation process is the main objective of the European project Laboranova. I began to collaborate within the project on September 2009 and my main objective has been to achieve this objective. Xpertum is the result of my work and my contribution to develop a web-based tool that the organizations can use to confront the challenges of the future. This document has been divided in 2 parts, the research and the prototype documentation. In the research part, I explain all the theoretical concepts that support the design and the functionalities of Xpertum and, in the prototype documentation part, I describe technical documentation, produced in the design tool step, that I have used to develop Xpertum

A General Introduction To Graph Visualization Techniques

Generally, a graph is an abstract data type used to represent relations among a given set of data entities. Graphs are used in numerous applications within the field of information visualization, such as VLSI (circuit schematics), state-transition diagrams, and social networks. The size and complexity of graphs easily reach dimensions at which the task of exploring and navigating gets crucial. Moreover, additional requirements have to be met in order to provide proper visualizations. In this context, many techniques already have been introduced. This survey aims to provide an introduction on graph visualization techniques helping the reader to gain a first insight into the most fundamental techniques. Furthermore, a brief introduction about navigation and interaction tools is provided

Scalability considerations for multivariate graph visualization

Real-world, multivariate datasets are frequently too large to show in their entirety on a visual display. Still, there are many techniques we can employ to show useful partial views-sufficient to support incremental exploration of large graph datasets. In this chapter, we first explore the cognitive and architectural limitations which restrict the amount of visual bandwidth available to multivariate graph visualization approaches. These limitations afford several design approaches, which we systematically explore. Finally, we survey systems and studies that exhibit these design strategies to mitigate these perceptual and architectural limitations

Measuring and improving the readability of network visualizations

Network data structures have been used extensively for modeling entities and their ties across such diverse disciplines as Computer Science, Sociology, Bioinformatics, Urban Planning, and Archeology. Analyzing networks involves understanding the complex relationships between entities as well as any attributes, statistics, or groupings associated with them. The widely used node-link visualization excels at showing the topology, attributes, and groupings simultaneously. However, many existing node-link visualizations are difficult to extract meaning from because of (1) the inherent complexity of the relationships, (2) the number of items designers try to render in limited screen space, and (3) for every network there are many potential unintelligible or even misleading visualizations. Automated layout algorithms have helped, but frequently generate ineffective visualizations even when used by expert analysts. Past work, including my own described herein, have shown there can be vast improvements in network visualizations, but no one can yet produce readable and meaningful visualizations for all networks. Since there is no single way to visualize all networks effectively, in this dissertation I investigate three complimentary strategies. First, I introduce a technique called motif simplification that leverages the repeating patterns or motifs in a network to reduce visual complexity. I replace common, high-payoff motifs with easily understandable glyphs that require less screen space, can reveal otherwise hidden relationships, and improve user performance on many network analysis tasks. Next, I present new Group-in-a-Box layouts that subdivide large, dense networks using attribute- or topology-based groupings. These layouts take group membership into account to more clearly show the ties within groups as well as the aggregate relationships between groups. Finally, I develop a set of readability metrics to measure visualization effectiveness and localize areas needing improvement. I detail optimization recommendations for specific user tasks, in addition to leveraging the readability metrics in a user-assisted layout optimization technique. This dissertation contributes an understanding of why some node-link visualizations are difficult to read, what measures of readability could help guide designers and users, and several promising strategies for improving readability which demonstrate that progress is possible. This work also opens several avenues of research, both technical and in user education

Contours in Visualization

This thesis studies the visualization of set collections either via or defines as the relations among contours. In the first part, dynamic Euler diagrams are used to communicate and improve semimanually the result of clustering methods which allow clusters to overlap arbitrarily. The contours of the Euler diagram are rendered as implicit surfaces called blobs in computer graphics. The interaction metaphor is the moving of items into or out of these blobs. The utility of the method is demonstrated on data arising from the analysis of gene expressions. The method works well for small datasets of up to one hundred items and few clusters. In the second part, these limitations are mitigated employing a GPU-based rendering of Euler diagrams and mixing textures and colors to resolve overlapping regions better. The GPU-based approach subdivides the screen into triangles on which it performs a contour interpolation, i.e. a fragment shader determines for each pixel which zones of an Euler diagram it belongs to. The rendering speed is thus increased to allow multiple hundred items. The method is applied to an example comparing different document clustering results. The contour tree compactly describes scalar field topology. From the viewpoint of graph drawing, it is a tree with attributes at vertices and optionally on edges. Standard tree drawing algorithms emphasize structural properties of the tree and neglect the attributes. Adapting popular graph drawing approaches to the problem of contour tree drawing it is found that they are unable to convey this information. Five aesthetic criteria for drawing contour trees are proposed and a novel algorithm for drawing contour trees in the plane that satisfies four of these criteria is presented. The implementation is fast and effective for contour tree sizes usually used in interactive systems and also produces readable pictures for larger trees. Dynamical models that explain the formation of spatial structures of RNA molecules have reached a complexity that requires novel visualization methods to analyze these model\''s validity. The fourth part of the thesis focuses on the visualization of so-called folding landscapes of a growing RNA molecule. Folding landscapes describe the energy of a molecule as a function of its spatial configuration; they are huge and high dimensional. Their most salient features are described by their so-called barrier tree -- a contour tree for discrete observation spaces. The changing folding landscapes of a growing RNA chain are visualized as an animation of the corresponding barrier tree sequence. The animation is created as an adaption of the foresight layout with tolerance algorithm for dynamic graph layout. The adaptation requires changes to the concept of supergraph and it layout. The thesis finishes with some thoughts on how these approaches can be combined and how the task the application should support can help inform the choice of visualization modality

A Coloring Algorithm for Disambiguating Graph and Map Drawings

Drawings of non-planar graphs always result in edge crossings. When there are many edges crossing at small angles, it is often difficult to follow these edges, because of the multiple visual paths resulted from the crossings that slow down eye movements. In this paper we propose an algorithm that disambiguates the edges with automatic selection of distinctive colors. Our proposed algorithm computes a near optimal color assignment of a dual collision graph, using a novel branch-and-bound procedure applied to a space decomposition of the color gamut. We give examples demonstrating the effectiveness of this approach in clarifying drawings of real world graphs and maps

A visual multivariate dynamic egocentric network exploration tool

Visualizing multivariate dynamic networks is a challenging task. The evolution of the dynamic network within the temporal axis must be depicted in conjunction with the associated multivariate attributes. In this thesis, an exploratory visual analytics tool is proposed to display multivariate dynamic networks with spatial attributes. The proposed tool displays the distribution of multivariate temporal domain and network attributes in scattered views. Moreover, in order to expose the evolution of a single or a group of nodes in the dynamic network along the temporal axis, an egocentric approach is applied in which a node is represented with its neighborhood as an ego-network. This approach allows users to observe a node's surrounding environment along the temporal axis. On top of the traditional ego-network visualization methods, such as timelines, the proposed tool encodes ego-networks as feature vectors consisting of the domain and network attributes and projects them onto 2D views. As a result, distances between projected ego-networks represent the dissimilarity across temporal axis in a single view. The proposed tool is demonstrated with a real-world use case scenario on merchant networks obtained from a one-year long credit card transaction