1. VISUALIZATION - 10 Pavel Slavík

2. ENV 2006 3.2 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)

3. ENV 2006 3.3 Brushing as a Solution Brushing selects a restricted range of one or more variables Selection then highlighted

4. ENV 2006 3.4 Parallel Coordinates Brushing picks out the high MPG data

5. GRAPH VISUALIZATION Visualization Course OI 5

6. What is a graph? Visualization Course OI 6

7. 7 © 2012 Prof. Dr. Franz J. Brandenburg Graph Drawing 1 7 2 3 4 5 6 8 Synonyms: Graph network diagram schema map 12 34 56 78 3-D 12 34 56 78 planar

8. 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

9. Usage of Graphs Visualization Course OI 9

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11. Visualization Course OI 11

12. Example - Phone fraud Visualization Course OI 12

13. Visualization Course OI 13

14. Visualization Course OI 14

15. TREE VISUALIZATION Visualization Course OI 15

16. Tree visualization Visualization Course OI 16

17. Tree Maps Visualization Course OI 17

18. TreeMaps Space-filling technique that divides space recursively Segments space according to ‘size’ of children nodes map of the market – smartmoney.com Visualization Course OI 18

19. Treemap applied to File System Visualization Course OI 19

20. 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 OI 20

21. Cone Trees Tree layout in three dimensions Shadows provide 2D structure cone tree – robertson, mackinlay, and card Visualization Course OI 21

22. Hyperbolic Trees Visualization Course OI 22

23. Visualization Course OI 23

24. Tree Visualization Ball-and-stick visualization: use the position and appearance of the glyphs Rooted-Tree Layout of the FFmpeg software Visualization Course OI 24

25. Tree Visualization Radial-Tree Layout Visualization Course OI 25

26. Tree Visualization 3D Cone-Tree Layout Visualization Course OI 26

27. NETWORK VISUALIZATION Visualization Course OI (27)

28. 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 OI 28

29. Traditional Approach To reduce cluttering of data (traditional) –Aggregation: for large numbers of links or nodes –Thresholding: for detecting changes Visualization Course OI 29

30. Internet traffic Visualization Course OI 30

31. Arc Map with parameterization of arc height Add translucency of arc &, coloring and size glyphs of countries Visualization Course OI 31

32. Static Displays (LinkMap) Focus on one Node (Oakland) Visualization Course OI 32

33. Static Displays (LinkMap) Include all nodes (10% of links shown) Visualization Course OI 33

34. 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 OI 34

35. Network visualization Often uses physics models (e.g., edges as springs) to perform layout. Can be animated and interacted with. Visualization Course OI 35

36. Six Degrees of Mohamed Atta http://business2.com/articles/mag/0,1640,35253,FF.html http://business2.com/articles/mag/0,1640,35253,FF.html Visualization Course OI 36

37. Parameter classes Statistics Levels Geography / topology Time Aggregation Size Color Visualization Course OI 37

38. 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 OI 38

39. GRAPH DRAWING Visualization Course OI (39)

40. 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 OI 40

41. 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 OI 41

42. 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

43. 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

44. Force-directed Layout Source: www.visualthesaurus.comwww.visualthesaurus.com Also known as: Spring Spreads nodes –Minimizes chance of node occlusion

45. Example A graph drawing through a number of iterations of a force directed algorithm.

46. Graph Layout: The Problem Visualization Course OI 46

47. Graph Layout: The Problem Visualization Course OI 47

48. Traditional Graph Drawing Visualization Course OI poly-line graphs planar, straight-line drawing orthogonal drawing upward drawing of DAGs 48

49. Graph based techniques Visualization Course OI 49

50. 2D Graph Examples Visualization Course OI 50

51. 2D Graph Examples Visualization Course OI 51

52. 3D-Graph Drawing Visualization Course OI 52

53. Visualization Course OI 53 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.

54. Visualization Course OI 54

55. Graph layout Visualization Course OI 55 Graphs are ubiquitous models. –Networks, protocols, schemas, web, software… Effective visualization techniques match tasks, perception and algorithms. hierarchical force-directed orthogonal symmetric

56. Hierarchical drawing: finite state machine (protocol) Visualization Course OI 56 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

57. 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 OI 57

58. 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 OI 58

59. 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 OI 59

60. Call Graph using a Force-Directed Layout Graph Visualization Visualization Course OI 60

61. 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

62. Minimum spanning tree Visualization Course OI 62

63. Hierarchical graph layout Visualization Course OI 63 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

64. Hierarchical Graph Layout Visualization Course OI Evolution of the UNIX operating system Hierarchical layering based on descent 64

65. Hierarchical graph layout Visualization Course OI Gnutella network 65

66. Radial Layout Visualization Course OI 66 Animated Exploration of Graphs with Radial Layout, Yee et al., 2001 Gnutella network

67. Graph Visualization Problems Visualization Course OI 67

68. AESTHETICS OF GRAPH Visualization Course OI 68

69. How to make a nice graph Visualization Course OI 69

70. 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

71. Graph Drawing Methods: Concepts Crossings: minimization of the total number of crossings. – Ideally we would have planar graphs (not always possible).

72. 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

73. 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.

74. 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.

75. Graph Drawing Methods: Concepts Angular resolution: Maximization of the smallest angle between two edges incident on the same vertex.

76. Graph Drawing Methods: Concepts Aspect Ratio: minimization of the aspect ratio of the drawing L2 L1 A.R. = L2/L1

77. Graph Drawing Methods: Concepts Symmetry:display the symmetries of the graph in the drawing

78. Graph Drawing Methods: Concepts Most aesthetics are associated with optimization problems – most of them computationally hard. Approximation strategies and heuristics for real- time response.

79. Graph Visualization Force-Directed LayoutSplatting; Dense Representation Visualization Course OI 79

80. Visualization Course OI 80 Thank you for your attention Pavel Slavík, 5.9.2015

81. Circular Layouts (1 circle) Ex: Schemaball –Database schema –Tables connected via foreign keys Source: http://mkweb.bcgsc.ca/schemaball/?home Schemaball, Martin Krzywinski