Upload
eri-zuliarso
View
246
Download
3
Tags:
Embed Size (px)
DESCRIPTION
graph visualization algorithm
Citation preview
Graph Visualization: A Survey
Overview Applications, Key Issues Graph Layout Navigation and Interaction Clustering Systems Current State of Graph Visualization
ReferenceI.Herman, G. Melancon, M.S. Marshall, Graph Visualization and Nav-igation in Information Visualization: A Survey, IEEE Transactions onVisualization and Computer Graphics, Volume 6(1), January, 2000.ITCS 6010/8010: Information Visualization 1 Graph Visualization
Graph Visualization
Survey is focused on the use of graph visualization techniques toproblems in Information Visualization.
Graphs - a natural way to represent relationships. Graphs in Infoviz: Are there inherent relationships among the input
data elements? NO: Unstructed Data - Infoviz must be used to discover relation-
ships. YES: Graphs can be used to represent the relationships - data
elements (nodes) and edges (relationships). Survey is focused on structured data and the use of graphs applied
to Infoviz domain.
ITCS 6010/8010: Information Visualization 2 Graph Visualization
Applications
File hierarchies, organization charts, biological taxonomies Web site maps, browsing history Biology: Evolutionary, phylogenetic trees, genetic maps, biochemi-
cal pathways, protein function Computer Science: data structures, object oriented systems, ER
diagrams, scene graphs (graphics)
ITCS 6010/8010: Information Visualization 3 Graph Visualization
Key Issues in Graph Visualization
Size is the key issue in visualizing graphs. Large graphs are constrained by display resources, and usability
(interaction, for instance) Very little work on applying cognitive science or human factors.
ITCS 6010/8010: Information Visualization 4 Graph Visualization
Graph Layout Algorithms
Background: Graph DrawingGiven a set of nodes and a set of edges (relations), calculate the positionof the nodes and the curve to be drawn for each edge. Well studied subject (hundreds of publications, books!) Planarity: Graphs drawn on a plane with no edge crossing Layout types: grid layouts (nodes at integer coords), force-directed
models, simulated annealing based layouts. Aesthetic Issues: Nodes, edges evenly distributed, isomorphic sub-
structures, straight line edges, etc.
ITCS 6010/8010: Information Visualization 5 Graph Visualization
Example Tree Layout
Reingold and Tilford Algorithm
Isomorphic subtrees are always laid out the same way Distance between nodes is a parameter.ITCS 6010/8010: Information Visualization 6 Graph Visualization
Layout Algorithm Issues
Size: Graphs with thousands of nodes can make most layout algo-rithms almost useless.
NicheWorks, H3Viewer are among systems that can handle largegraphs.
High Node Density: Traditional algorithms cannot scale up, makinginteraction difficult.
Can also use 3D layouts or non-Euclidean geometry. Extremely large graphs - need methods to simplify (reduce) graph
size (clustering, grouping)
ITCS 6010/8010: Information Visualization 7 Graph Visualization
Layout Algorithm Issues (contd) Predictability: Consecutive runs of an algorithm should not result in
radically different visual representations (preserving mental map) Time Complexity: Real-time (or near real-time) updates of the graph
is needed in highly interactive applications, where the graph can bemodified.
ITCS 6010/8010: Information Visualization 8 Graph Visualization
Traditional Layout
Child nodes below common ancestor Reingold and Tilford algorithm - the best known - can produce top-
down or lef to right layouts, as well as grid positioning. H-Tree: Representation for binary trees; uses axis-aligned repre-
sentaton of edges. Radial Trees (Eades) Balloon Views - planarized Cone Trees Tree maps, Onion Graphs, Cushion Treemaps
ITCS 6010/8010: Information Visualization 9 Graph Visualization ITCS 6010/8010: Information Visualization 10 Graph Visualization
ITCS 6010/8010: Information Visualization 11 Graph Visualization
Traditional Layout (contd) Spring Layouts: or force-directed Models nodes and edges as physical bodies tied with springs. Uses Hookes law to define forces between bodies Can lead to well balanced layouts, some optimzed for minimizing
edge crossings and predictable layouts. Disadvantage: Computational complexity is generally O(N 3),
most methods are highly unpredictable.
ITCS 6010/8010: Information Visualization 12 Graph Visualization
Spanning Trees
Most traditional layout algorithms work well on small graphs A practical solution is to layout the graph by computing the spanning
tree (tree layouts are typically of O(N) complexity). Once the tree is laid out, the other edges can then be added to tree. Methods: Can use breadth-first or depth-first search, starting from a likely
root node. If edges have weight, can use various optimization criteria (and
heuristics) in the layout algorithm
ITCS 6010/8010: Information Visualization 13 Graph Visualization
3D Layouts
3D layouts, in combination with interactive viewing can accommo-date larger graphs, while compensating for occlusion
Most force-directed and simulated annealing approaches can alsobe extended to 3D.
3D layouts also use visual cues such as transparency, depth queu-ing, etc.
Classic Example: Cone Trees (a direct 3D algorithm) and their ex-tensions (disk trees)
ITCS 6010/8010: Information Visualization 14 Graph Visualization
3D Radial Layout
ITCS 6010/8010: Information Visualization 15 Graph Visualization
Cone Trees
ITCS 6010/8010: Information Visualization 16 Graph Visualization
Other 3D Layout Examples
SGI file system navigator (until version 5) (seen in Jurassic Park!) Perspective Wall - data representation as posters on large walls Viznet, Vitesse - data mapped onto a sphere
Difficulties with 3D layouts 3D navigation in 2D displays and 2D input devices VR and immersive environments are not commonplace
ITCS 6010/8010: Information Visualization 17 Graph Visualization
Hyperbolic Layouts
Provides a distorted view of a tree in 2D or 3D, similar to fish-eyeviews
Makes it possible to view and interact with large trees, and thus cru-cial for real-life Infoviz applications.
A mapping from hyperbolic to Euclidean space - two models, Kleinand Poincare.
ITCS 6010/8010: Information Visualization 18 Graph Visualization
Hyperbolic Layouts(contd) Klein Model: Klein model uses an open disc (sphere in 3d) as a subset -
hyperbolic plane contains points internal to the disc Line segments of equal length in hpyerbolic plane get exponen-
tially smaller as they approach the perimeter Poincare Model: Similar to the Klein model, but segments are arcs,
intersecting orthogonally at the perimeter of the disc.
ITCS 6010/8010: Information Visualization 19 Graph Visualization
Hyperbolic Layouts(contd)
Hyperbolic Layouts(contd)
ITCS 6010/8010: Information Visualization 20 Graph Visualization
Hyperbolic Layouts(contd)
The small wedges seen in Euclidean plane (resulting in unusablelayouts is very different in the hyperbolic plane (wedges are openedup)
ITCS 6010/8010: Information Visualization 21 Graph Visualization
Navigation and Interaction
Crucial tools to dealing with large graphs Can help reveal graph structure Real-time interaction is an important goal.
ITCS 6010/8010: Information Visualization 22 Graph Visualization
Zoom and Pan
Standard graphics interaction operations, manipulated by affinetransformations, followed by a redraw.
Geometric zoom vs. Semantic Zoom. Zooming in, can cause loss of context
ITCS 6010/8010: Information Visualization 23 Graph Visualization
Space-Scale Diagrams
Represent points in image as rays (with point, magnification) Choose paths to destination as a combination of zoom and pan ac-
tions
ITCS 6010/8010: Information Visualization 24 Graph Visualization
Focus+Context Techniques
Techniques that allow users to focus on some detail of the visualization,without losing context.Fisheye Distortion Simple distortions use a radial function, for eg.,
h(x) = (d + 1)/(d + 1/x)
ITCS 6010/8010: Information Visualization 25 Graph Visualization
Fisheye Distortion(contd)
ITCS 6010/8010: Information Visualization 26 Graph Visualization
Fisheye Distortion(contd)
ITCS 6010/8010: Information Visualization 27 Graph Visualization
Fisheye Distortion(contd) Cartesian Fisheye: Distortion applied to X and Y independently. Approximation of segments with linear elements can introduce edge
crossings.
ITCS 6010/8010: Information Visualization 28 Graph Visualization
Focus+Context and Layout
Fisheye distortion is typically a processing step separate from thelayout.
Hyberbolic layout is the exception, as the technique is designed withthe goal of focus+context.
Hyperbolic layouts - changing focus is equivalent to changing thecenter of the Euclidean circle(sphere).
Other Examples: mapping onto spheres and ellipsoids, followed byperspective projection, Perspective Wall.
ITCS 6010/8010: Information Visualization 29 Graph Visualization
Clustering
Advantageous to reduce the number of elements displayed, espe-cially very large graphs/trees.
Structure-based clustering: uses only structural information aboutthe graph
Content-based clustering: node and edge attributes are used to de-termine clusters.
Most clustering work is structure based. Clustering - used to accomplish filtering and search.
ITCS 6010/8010: Information Visualization 30 Graph Visualization
Clustering Approaches
Locate disjoint clusters (simpler to navigate) Choose clusters with the least number of edges between members
(Ratio-Cut technique) Hierarchical clustering
ITCS 6010/8010: Information Visualization 31 Graph Visualization
Cluster Layout
Can just layout the clusters by themselves - good high level view ofthe graph structure
Use glyphs to represent clusters and treat them as supernodeswith abridgemens between clusters.
Force-directed cluster layout: nodes that are related to each otherare attracted, while all nodes have a minimal repulsion force (O(N 3)complexity).
ITCS 6010/8010: Information Visualization 32 Graph Visualization
Node Metrics for Clustering
Structure or content based. Combination of structure and content based metrics are more pow-
erful, eg. linear weighted combination. Representation of unselected nodes Ghosting - deemphasizing nodes Hiding Grouping - grouping under a new super-node representation
ITCS 6010/8010: Information Visualization 33 Graph Visualization
Cluster Representation
ITCS 6010/8010: Information Visualization 34 Graph Visualization
Graph Drawing - Systems, Journals,Conferences
A very large community of researchers, users Large number of systems have been implemented Graph Drawing Symposia - dedicated to this domain Journal of Graph Algorithms and Applications Significant ties to CHIXX, UISTXX, InfoVizXX, IEEE TVCG, CG
Forum
ITCS 6010/8010: Information Visualization 35 Graph Visualization