IAT 355 Intro to Visual Analytics Graphs, trees and networks 2. Lyn Bartram

Transcription

1 IAT 355 Intro to Visual Analytics Graphs, trees and networks 2 Lyn Bartram

2 Graphs and Trees: Connected Data Graph Vertex/node with one or more edges connecting it to another node Cyclic or acyclic Edge can be weighted (value) or categorized Tree Undirected graph where two nodes are connected by only one edge used for hierarchy Rooted or unrooted Edge can be weighted (value) or categorized

3 Design choices Connectivity Node-link graphs Good for finding pairwise/multiway relations Good for following paths through structure Force-directed placement Containment Effective at showing hierarchical structure Good for finding attributes of leaf nodes Treemaps, nested views Matrices

4 Connectivity example Idiom What Data Network Force-directed placement How Encode Nodes: point marks Links: connection marks Why Tasks Understand topological structure Path following Scale Nodes: dozens/hundreds Edges: hundreds Node/edge density: E < 4N T. Munzner, Visualization Analysis and Design, DRAFT 2014

5 Node-link diagrams

6 Connectivity: Issues Scale Structure Value occlusion

7 Containment example Idiom treemap What Data Tree How Encode area marks, containment, rectilinear Why Tasks Understand hierarchicalstructure query attributes at leaf nodes Scale Nodes: IM Edges: 1M T. Munzner, Visualization Analysis and Design, DRAFT 2014

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9 Containment Containment can use spatial position to encode Tree attributes Depth Parent-child position T. Munzner, Visualization Analysis and Design, DRAFT 2014

10 Radial layouts:dendrogram Leaf nodes at same level More efficient use of screen space

11 Composite approaches Use hierarchical structure to reduce connectivity complexity Hierarchy can be derived computationally or by user interaction

12 Computational hierarchy Coarsen network into derived hierarchy of successively simpler networks Edge colour shows length between clusters Orange/yellow dense Increases scale 7220 nodes, links

13 User-defined hierarchy Users can explore multiple different hierarchies Constraints of subgraphs, or slices through the hierarchy, have to be established Reduces rendering and interpretation complexity

14 User-defined hierarchies: Grouse Flocks T. Munzner, Visualization Analysis and Design, DRAFT 2014

15 Tree-based graph layout 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

16 Tree-ify the graph

17 Tree-ify the graph

18 Hierarchical graph layout 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 The method used in graphviz s dot algorithm Great for directed acyclic graphs, but often misleading in the case of cycles

19 Hierarchical Graph Layout Evolution of the UNIX operating system Hierarchical layering based on descent

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21 Hierarchical graph layout Gnutella network

22 Typical Sugiyama layout (dot) - preserves tree structure Alternative method - preserves uniform edge lengths slide borrowed from Tim Dwyer and Marti Hearst

23 slide borrowed from Tim Dwyer Examples

24 Radial Layout Animated Exploration of Graphs with Radial Layout, Yee et al., 2001 Gnutella network

25 semi-hierarchical networks

26 Arc diagrams 1D node layout Ordering affords views of clusters, cliques and bridges Ordering requires seriation

27 Perceptual scalability and link density Weakness of node-link graphs : link density # links compared to # nodes Link density > 4 for any reasonable graph is unreadable [Melancon 06] Filtering, user interaction, clustering mitigate but do not remove hairball issue

28 Matrices Combine ability to derive leaf atttributes (containment) and topological structure (connectivity) Perceptually scaleable Link density can equal E = N 2

29 Matrices 20 Years of Four HCI Conferences: A Visual Exploration Henry et al. IJHCI 2007

30 Matrices with Submatrices [N. Henry]

31 Matrices Pros Eliminate occlusion Perceptual scalability predictability (screen space) stability (adding elements causes only small change) zooming Easy reordering Quick estimation Fast node lookup (spatial indexing) Cons Unfamiliar! Training and practice required Indirect representation of links means topological structure has to be visually constructed rather than immediately seen Can become visually dense

32 Characteristic patterns in matrix views and node-link views. a) Hub nodes connecting several clusters. b) Cluster. c) Clique: cluster of fully interconnected nodes. From [Henry and Fekete 06],

33 Hybrid approach: Matrix Explorer

34 Distortion techniques: fisheye Based on camera fisheye lens model Original 1D Furnas Distort screen space around area of interest FOCUS Use interaction to expand and collapse sub-graphs HIERARCHY Continuous Zoom (levels of hierarchy) EPS (continuous detail)

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36 Hyperbolic Browser: Inspiration

37 Using Distortion and Focus + Context The Hyperbolic Tree Browser The Hyperbolic Browser: A Focus + Context Technique for Visualizing Large Hierarchies, Lamping & Rao, CHI Uses non-euclidean geometry as basis of focus + context technique The hyperbolic browser is a projection into a Euclidean space a circle Exponential growth in space available with linear growth of radius Makes tree layout easy Size of objects decreases with growth of radius Reduces expense of drawing trees when cut-off at one pixel

38 Initial Layout Root mapped at center Multiple generations of children mapped out towards edge of circle Drawing of nodes cuts off when less than one pixel

39 User orientation on refocus Problem Hyperbolic Geometry can allow disorienting rotations of objects when refocusing Solution one: Preserve initial angular orientation of parent to child nodes Solution two: Preserve left to right orientation of parent to child nodes beginning with initial display Note: both rely on relative geometric consistency

40 User orientations - Solutions Preserving Angular Orientation Left to Right Ordering

41 Structurally-Independent Layout Ignore the graph structure. Base the layout on other attributes of the data Examples: Geography Time Benefits Often very quick layout Optimizes communication of particular features Drawbacks May or may not present structure well

42 Structurally-Independent Layout Ignore the graph structure. Base the layout on other attributes of the data Examples: Geography Time Benefits Often very quick layout Optimizes communication of particular features Drawbacks May or may not present structure well

43 Structurally Independent Layout The Skitter Layout Internet Connectivity Angle = Longitude geography Radius = Degree # of connections Skitter,

44 Progressive Disclosure Only show subsets that are currently selected wordnet/wordnet2.html

45 Problem: Multivariate Graphs What if you want to associate information with the nodes and edges? Typical approach: vary Size of nodes Color of nodes Fatness of edges Colors of edges However, it s hard to make quantitative comparisons when these retinal cues are spread throughout the graph.

46 Solution: Wattenberg s Pivot Graphs Focuses on relationship between node attributes and connections Aggregate all nodes that have the same values on each of those dimensions, and aggregate edges accordingly. In graph below, F = Female, M = Male, Numbers mean counts Visual Exploration of Multivariate Graphs, Wattenberg, IEEE Infoviz???

47 Multidimensional Pivot Graphs What is added, and what is lost, from this transformation?

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49 Compare 2D Pivot Graph with 2D Matrix

50 Issues with Pivot Graphs Disconnected components may become connected Acyclic graphs may obtain cycles

51 New toolkits! Networks for excel by Marc Smith et al. at Microsoft research Used to be called.netmap Now called NodeXL Requires windows-specific software (Search on excel NodeXL ) Chart Tamer for Excel Stephen Few et al.

52 .NetMap: Edges Worksheet

53 .NetMap: Vertices Worksheet

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55 Marc s Facebook Graph

56 Chart Tamer Stephen Few + XL 3 Function-based

57 Summary Networks are a big topic! Many approaches to layout. New ideas still coming all the time.