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VISUALIZATION - 10Pavel Slavík
ENV 20063.2
The Screen Space Problem
All techniques, sooner or later, run out of screen space
Parallel co-ordinates– Usable for up to 150
variates– Unworkable greater than
250 variates
Remote sensing: 5 variates, 16,384 observations)
ENV 20063.3
Brushing as a Solution
Brushing selects a restricted range of one or more variables
Selection then highlighted
ENV 20063.4
Parallel Coordinates
Brushing picksout the high MPGdata
GRAPH VISUALIZATION
Visualization Course OI5
What is a graph?
Visualization Course OI6
7© 2012 Prof. Dr. Franz J. Brandenburg
Graph Drawing
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723
4
5
6
8
Synonyms: Graph network diagram schema map
1 2
34
5 6
78
3-D
1 2
34
5 6
78
planar
Information Visualization. Graph Drawing
Graph Drawing– Old topic, many books, etc.– May have other goals than visualization
• E.g. VLSI design
Graph Visualization– Size key issue– Usability requires nodes to be discernable– Navigation considered
Usage of Graphs
Visualization Course OI9
Visualization Course OI10
Visualization Course OI11
Example - Phone fraud
Visualization Course OI12
Visualization Course OI13
Visualization Course OI14
TREE VISUALIZATION
Visualization Course OI15
Tree visualization
Visualization Course OI16
Tree Maps
Visualization Course OI17
TreeMaps
Space-filling technique that divides space recursively
Segments space according to ‘size’ of children nodes
map of the market – smartmoney.com
Visualization Course OI18
Treemap applied to File System
Visualization Course OI19
Treemap Problems
Too disorderly– What does adjacency mean?– Aspect ratios uncontrolled leads to lots of skinny boxes
that clutter
Hard to understand– Must mentally convert nesting to hierarchy descent
Color not used appropriately Wrong application
– Don’t need all this to just see the largest files in the OS
Visualization Course OI20
Cone Trees
Tree layout in three dimensions
Shadows provide 2D structure
cone tree – robertson, mackinlay, and card
Visualization Course OI21
Hyperbolic Trees
Visualization Course OI22
Visualization Course OI23
Tree Visualization
• Ball-and-stick visualization: use the position and appearance of the glyphs
Rooted-Tree Layout of the FFmpeg softwareVisualization Course OI24
Tree Visualization
Radial-Tree LayoutVisualization Course OI25
Tree Visualization
3D Cone-Tree LayoutVisualization Course OI26
NETWORK VISUALIZATION
Visualization Course OI(27)
Goal
Visualize the data associated with a network– Understand data, not network themselves
Coping with large data volumes– Hundreds of nodes– Thousands of links– Data from time periods
Overcome the map clutter problem
Visualization Course OI28
Traditional Approach
To reduce cluttering of data (traditional)
– Aggregation: for large numbers of links or nodes
– Thresholding: for detecting changes
Visualization Course OI29
Internet traffic
Visualization Course OI30
Arc Map with parameterization of arc height
Add translucency of arc &, coloring and size glyphs of countries
Visualization Course OI31
Static Displays (LinkMap)
Focus on one Node (Oakland)Visualization Course OI32
Static Displays (LinkMap)
Include all nodes (10% of links shown)Visualization Course OI33
Example (zoom in Link Map)
Left: All line segments intersecting the display Middle: any line segments with at least one endpoint
in the display Right: only lines that both begin and end inside the
display
Visualization Course OI34
Network visualization
Often uses physics models (e.g., edges as springs) to perform layout.
Can be animated and interacted with.
Visualization Course OI35
Six Degrees of Mohamed Attahttp://business2.com/articles/mag/0,1640,35253,FF.html
Visualization Course OI36
Parameter classes
Statistics Levels Geography / topology Time Aggregation Size Color
Visualization Course OI37
Issues with parameter focusing
Space of parameters large Combination of parameters to choose Displays sensitive to particular parameter values
SOLUTION– Allow Direct manipulation of parameters
Visualization Course OI38
GRAPH DRAWING
Visualization Course OI(39)
History of Graph Drawing
Euler used a drawing to solve the Königsberger Brückenproblem (1736)
Symposia on Graph Drawing initiated 1992 Issues
– Planarity • No edges cross in 2D
– Aesthetic rules• Edges should have same length• Edges should be straight lines• Isomorphic substructures displayed equivalently
Visualization Course OI40
Tasks Related to Graph Drawing
Layering a graph Turning graph into directed acyclic graph Planarizing (achieve that no edges cross) Minimizing area Minimizing number of bends in edges
But Algorithms too complex for large graphs
Visualization Course OI41
Graph Drawing Aesthetics
Minimize edge crossings Draw links as straight as possible Maximize minimum angle Maximize symmetry Minimize longest link Minimize drawing area Centralize high-degree nodes Distribute nodes evenly Maximize convexity (of polygons) …
Source: [9] Davidson & Harel
Node Placement Methods
Node-link diagrams– Force-directed– Geographical maps– Circular layouts
• One or multiple concentric
– Clustering– Layouts based on node attributes (later)
Matrix-based representations
Force-directed Layout
Source: www.visualthesaurus.com
Also known as: Spring
Spreads nodes– Minimizes
chance of node occlusion
Example
A graph drawing through a number of iterations of a force directed algorithm.
Graph Layout: The Problem
Visualization Course OI46
Graph Layout: The Problem
Visualization Course OI47
Traditional Graph Drawing
Visualization Course OI
poly-line graphs
planar, straight-line drawing
orthogonal drawing
upward drawing of
DAGs48
Graph based techniques
Visualization Course OI49
2D Graph Examples
Visualization Course OI50
2D Graph Examples
Visualization Course OI51
3D-Graph Drawing
Visualization Course OI52
Visualization Course OI53
Solutions for your logic and mechanical puzzles
"Dear Archimedes Lab, if you have 3 houses and each need to have water, gas and electricity connected, is it possible to do so without crossing any lines? Can you please post the solution? Thank you very much!" -- Gerald
Category: Topological graph theory.
Visualization Course OI54
Graph layout
Visualization Course OI55
Graphs are ubiquitous models.– Networks, protocols, schemas, web, software…
Effective visualization techniques match tasks, perception and algorithms.
hierarchicalforce-directed
orthogonal
symmetric
Hierarchical drawing: finite state machine (protocol)
Visualization Course OI56
Layout is made by a series of optimizations.
Geometric and topological objectives such as edge length and crossings are ‘optimized’
Gansner, North, Vo, after Sugiyama
Hierarchical layout Force-directed layout
Two images of the same network
Much of the difficulty with automatic layout problems rests in seeing the problem as uniform. Contrast two well known models: a hierarchical layout and a force-directed layout.
What makes a good visualization?
Visualization Course OI57
Much of the difficulty with automatic layout problems rests in seeing the problem as uniform. Contrast two well known models: a hierarchical layout and a force-directed layout.
Hierarchical layout Force-directed layout
Two images of the same network
What makes a good visualization?
Visualization Course OI58
Force-Directed Layout• The principle is to minimize the energy of the layout• The physical analogy is that every node in the graph is a charged
electric particles and every edge is an elastic spring• Nodes connected by edges will exert an attraction force• All nodes will exert a repelling force on each other, regardless of
whether they are connected or not• For each node, calculate the total force acting upon it• Move the position of the mode along the direction of the force• Do this process for every node• Repeat the above force-directed movement iteratively• Until it converges into a layout that has minimal forces for nodes,
thus the minimal energy of the layout
Graph Visualization
Visualization Course OI59
Call Graph using a Force-Directed Layout
Graph Visualization
Visualization Course OI60
Tree-based graph layout
Visualization Course OI
Select a tree-structure out of the graph– Breadth-first-search tree– Minimum spanning tree– Other domain-specific structures
Use a tree layout algorithm Benefits
– Fast, supports interaction and refinement
Drawbacks– Limited range of layouts
61
Minimum spanning tree
Visualization Course OI62
Hierarchical graph layout
Visualization Course OI63
Use directed structure of graph to inform layout Order the graph into distinct levels
– this determines one dimension
Now optimize within levels– determines the second dimension– minimize edge crossings, etc
Great for directed acyclic graphs, but often misleading in the case of cycles
Hierarchical Graph Layout
Visualization Course OI
Evolution of the UNIX operating system
Hierarchical layering based on descent
64
Hierarchical graph layout
Visualization Course OI
Gnutella network
65
Radial Layout
Visualization Course OI66
Animated Exploration of Graphs with Radial Layout, Yee et al., 2001
Gnutella network
Graph Visualization Problems
Visualization Course OI67
AESTHETICS OF GRAPH
Visualization Course OI68
How to make a nice graph
Visualization Course OI69
Graph Drawing Methods: Concepts
Aesthetics: specify graphic properties we would want to apply as much as possible to achieve readability.– Crossings– Area– Total / Maximum / Uniform Edge Length– Total / Maximum / Uniform Bends– Angular resolution– Aspect Ratio– Symmetry
Graph Drawing Methods: Concepts
Crossings: minimization of the total number of crossings.– Ideally we would have planar graphs (not always
possible).
Graph Drawing Methods: Concepts Area: minimization of the area of the drawing.
– Important to save screen space– Relevant just when we cannot arbitrarily scale the
graph down
Graph Drawing Methods: Concepts
Total Edge Length: minimization of the sum of the lengths of the edges.
Maximum Edge Length: minimization of the maximum length of an edge.– Both relevant just when we cannot arbitrarily scale the
graph down.
Uniform Edge Length: minimization of the variance of the lengths of the edges.
Graph Drawing Methods: Concepts
Total Bends: minimization of the total number of bends along the edges.– Important for orthogonal drawings– Trivially satisfied by straight-line drawings
Maximum Bends: minimization of the maximum number of bends on an edge.
Uniform Bends: minimization of variance of the number of bends on an edge.
Graph Drawing Methods: Concepts
Angular resolution: Maximization of the smallest angle between two edges incident on the same vertex.
Graph Drawing Methods: Concepts
Aspect Ratio: minimization of the aspect ratio of the drawing
L2
L1
A.R. = L2/L1
Graph Drawing Methods: Concepts
Symmetry:display the symmetries of the graph in the drawing
Graph Drawing Methods: Concepts
Most aesthetics are associated with optimization problems – most of them computationally hard.
Approximation strategies and heuristics for real-time response.
Graph Visualization
Force-Directed Layout Splatting;Dense Representation
Visualization Course OI79
Visualization Course OI80
Thank you for your attentionPavel Slavík, 19.04.2023
Circular Layouts (1 circle)
Ex: Schemaball– Database schema– Tables connected via
foreign keys
Source: http://mkweb.bcgsc.ca/schemaball/?home
Schemaball, Martin Krzywinski