1. Mining Networks through Visual Analytics
Incremental Hypothesis Building and Validation
Thanks. I thought the workshop was a good opportunity to present our work on graph visualization. We are not mining persons, althgough we do contribute to graph mining as part of the visualization process.
David Auber
Romain Bourqui
Guy Melançon
CNRS LaBRI UMR 5800 & INRIA Futurs – GRAVITÉ
Bordeaux, France

2. peacokmaps.com

3. Chinese proverb (?) “A picture is worth a thousand words” InfoVis
CyberInfraStructure
– Pajek
“A picture is worth a thousand words”
Chinese proverb (?)

4. Il y aurait encore le dessin le plus bête qui consiste à placer chaque feuille sur une coordonnée différente en abscisse. C’est l’économie que font Wetherell/Reingold et Tilford/Walker.
Tulip – BubbleTree

5. “It’s all visual” R. Feynman (Nobel prize in Physics)
Graph Viz Framework
Tulip
“It’s all visual”
R. Feynman (Nobel prize in Physics)

6. Internet traffic

7. “The purpose of computing is insight not numbers ”
Voronoï
Treemaps
“The purpose of computing is insight not numbers ”
R. Hamming (1973)

8. Cushion
Treemaps

9. “Visualization uses computer graphics to help provide insight on complicated problems, models or systems”
“Scientific visualization is exploring data and information graphically, gaining understanding and insights into the data”
R.A. Earnshaw (a pioneer in computer graphics, 1973)
Munzner’s Hyperbolic Browser

10. Tulip – Sugiyama Layout

11. Visualize? Inselberg – « creator » of parallel coordinates
« Insight through images »
« Goal: Visual Model to Help our Intuition »
« Involves: Geometry, Cognition, Art ? »

12. Visualize?

13. Visual graph mining related to security issues
“Recognize” structural properties
Identify key actors
Identify their neighborhood
Community structure
Connectivity between communities …
“Chess players recognize patterns”
I guess the issues I will discuss relate to security just as Tishby’s.

14. Example from NCTC data Extracted about 8000 incidents from WITS
Identified terrorists groups when possible (directly or through AFP)
Identified countries where incidents took place
Added territorial information (continents, world regions) to help organize the overall map

15. Example from NCTC data About 8000 incidents 9419 nodes 18486 edges
Layout is time consuming
Does not provide clue about structure
Filter out incidents with no identified group

16. Example from NCTC data Interactivity Tulip Graph Viz Framework
« Play » with network
Apply various metrics
Attribute-based node filtering
Tulip Graph Viz Framework
Opensource
Plug-in architecture

17. Massive data
Information big bang - Projet « How much information », Berkeley University
In 2001, about 1 exabyte (1 million terabytes) of data is generated annually worldwide, including % available only in digital form
In 2003 : each individual produces about 800 megabytes per year
We want to go for larger, more complex datasets. I certainly don’t have to bring in arguments to convince you of those needs. The figures reported by the Berkeley project or from Keim speak for themselves.

18. Massive data 100 million FedEx transactions / day
150 million VISA transactions / day
300 millions long distance calls / day over ATT’s network
35 billions s / day over the world
600 billions IP packets / day over DE-CIX backbone
Keim, VIEW Workshop 2006

19. Visualization and Moore’s law
Daniel Keim - Keynote Address, VIEW 2006

20. Visualization and Moore’s law
Issues that won’t be solved by hardware only
Design interaction together with visualization
Understand how and why visualization pays
Collaborate with other fields
Integrate visualization together with other technology
NIH-NSF Visualization Research Challenges Report, 2006

21. Added value of visual and interactive mining
KDD Panel «  The Perfect Data Mining Tool » [Ankerst 2002]
The human eye is an excellent tool for spotting natural patterns
Getting rid of the human in the loop? Wrong decision!
Increase human participation through visualization in the data exploration and knowledge discovery processes

22. « Sense making loop »
J. Thomas – Visual Analytics Initiative

23. « Visualization mantras »
Visual Information Seeking Mantra
Overview, Zoom-in / Filter, and Details on Demand (Shneiderman, 1996)
Visual Analytics Mantra
Analyse first, Show the Important, Zoom, filter and analyse, Details on demand (Keim 2006)

24. Visualization “pipeline”
A designer’s view on the visualization process

25. Protein interaction network (yeast); Barabàsi 2000
Visualize?
Protein interaction network (yeast); Barabàsi 2000

26. Organize data prior to visualization
Layer or hierarchize data based on:
node/edge metrics (eigenvalues, centralities, …)
topological feature detection
Use relevant drawing methods
Combine with interaction

27. Case study: ITA 2000 passenger air traffic
Cities connect through direct flights
Edge weights: number of passengers
Questions:
Read motivations of carriers through organization of the network?
Territorial logic?
Political? Economical?

28. Case study: ITA 2000 passenger air traffic
Cities connect through direct flights
Edge weights: number of passengers
Questions:
Read motivations of carriers through organization of the network?
Territorial logic?
Political? Economical?

29. TopoLayout – (Topological) Feature-based Hierarchization
Search the graph for components of growing complexity
Subtrees
Biconnected components (« blocks »)
Grid-like
« Clusters »

30. TopoLayout – (Topological) Feature-based Hierarchization
Search the graph for components of growing complexity
Subtrees
Biconnected components (« blocks »)
Grid-like
« Clusters »

31. TopoLayout – (Topological) Feature-based Hierarchization
Search the graph for components of growing complexity
Subtrees
Biconnected components
Grid-like
« Clusters »

32. TopoLayout – (Topological) Feature-based Hierarchization
Search the graph for components of growing complexity
Subtrees
Biconnected components
Grid-like
« Clusters »
Need to identify articulation points (“pivots”)
The graph builds into a “tree of biconnected components”

33. TopoLayout – (Topological) Feature-based Hierarchization
Search the graph for components of growing complexity
Subtrees
Biconnected components (« blocks »)
Grid-like (eigenvalues)
« Clusters »

34. TopoLayout – (Topological) Feature-based Hierarchization
Search the graph for components of growing complexity
Subtrees
Biconnected components (« blocks »)
Grid-like (eigenvalues)
« Clusters »

35. TopoLayout
Components naturally organize as a hierarchy through the search process

36. TopoLayout + interaction: Grouse
Explore the graph by unfolding/folding the hierarchy
The user’s navigation triggers layout of components
Higher level graphs (quotient graphs) are built from metanodes
Improve readability / Less visual elements
Faster layout, based on topology of quotient graph
Grouse

37. TopoLayout + interaction: Grouse
Multilevel hierarchy: recursive grouping of metanodes

38. TopoLayout + interaction: Grouse
Multilevel hierarchy: recursive grouping of metanodes

39. TopoLayout + interaction: Grouse
Multilevel Hierarchy for Abstraction: Cut

40. Multilevel navigation of small world networks
Small world networks: social networks, web graphs, transportation networks (ITA), …
Small world networks organize into several levels (hierarchy) [Adamic, Huberman]
Idea: capture the hierarchy and use it as a navigation paradigm

41. Small world networks Centralities Bottleneck passageways
Network organizes around those « pivots » nodes

42. Small world networks Centralities
Betweenness centrality has high computational cost (global)
Betweenness centrality
Eigenvalue centrality
Prefer local index
Degree
Edge strength

43. Small world networks
Edge strength: proportion of cycles containing an edge (length 3 and 4)
Mu = Nu\Nv
Mv = Nv\Nu
Wuv e u v
(Jaccard 1912)
(Tanimoto 1958)
Auber et al. 2003
Raddichi et al. 2004

44. Small world networks Edge strength
Costs linear time if degree is bounded, otherwise quadratic …
Mu = Nu\Nv
Mv = Nv\Nu
Wuv e u v

45. Small world networks Edge strength
Cost yet lower than most centralities (local versus global indices)
Incremental: local modification of graphs require local recomputation
Mu = Nu\Nv
Mv = Nv\Nu
Wuv e u v

46. Community structure of small world networks
Filter out weak edges
Capture components
Infer quotient graph (metanodes)
Recurse over each component

47. Community structure of small world networks
Filter out weak edges
Capture components
Infer quotient graph (metanodes)
Recurse over each component

48. Community structure of small world networks
Filter out weak edges:
Q. What threshold to choose?
A. Best possible one (!)
Use quality criteria
MQ (modularity quality)

49. “Quality” criteria MQ … …
C = (C1, C2, …, Cp) is a clustering of a graph G
MQ(C; G) = C1 C2 … Cp C1 C2 … Cp

50. MQ / Nice properties MQ varies over a bounded interval [-1, 1]
MQ behaves like a Gaussian distribution
MQ(C; G) =

51. MQ / Nice properties MQ behaves like a Gaussian distribution
MQ(C; G) =

52. Challenge: find the best possible clustering (according to MQ)
Exhaustive search: intractable
Optimization, search algorithms (hill climbing, genetic algorithms, bio-mimetics, …): costy
Heuristic: exploit node/edge centralities
Filter out weak edges
Tickmark possible values for edges
Find threshold with best MQ

53. Filter / Threshold 1 2 5 4 3

54. Filter / Threshold 1 2 5 4 3 

55. Filter / Threshold  C1 C2 C3 C4 C5
C()

56. Hierarchical organization of the network
The procedure can be iterated to produce a hierarchy of clusters
Strength of edges is recomputed at each stage
Threshold is locally chosen for each component

57. MQ / Extension To take into account the relative size of clusters
(MQ also naturally extends to fuzzy clustering)
MQ(C; G) =

58. MQ / Extension
Extend to various classes of graphs (where F stands for any adequate edge density function)
MQ(C; G) =

59. Conclusion – Future work
MQ / Extension to graph hierarchies

60. MQ / Extension to graph hierarchies
Inspired from attribute grammars

61. Conclusion – Future work
Study dynamic network
Streamed / Time-stamped network
Incremental/local computation/adjustment of
edge metrics (local metrics)
MQ (or other possible quality criteria)

62. Conclusion Interaction is the real added value of visualization
Must combine with other mining techniques
Insert combination in “sense making loop”

63. Conclusion
We are opened and interested to collaborate with colleagues from other areas, adopting different perspectives
Learning / Mining / …
Experts / Corporate organizations / Final users
Any idea for a different multilevel clustering criteria/approach?

64. Conclusion
We are opened and interested to collaborate with colleagues from other areas, with other perspectives
Learning / Mining / …
Experts / Corporate organizations / Final users
Go visit Tulip’s website and download the software (I’m here until Friday if you need a coach !)

65. Credits LaBRI UMR 5800, Bordeaux -- Equipe GRAVITÉ / INRIA Futurs
Guy Melançon
Maylis Delest
David Auber
Patrick Mary
Tulip Graph Viz Framework
R. Bourqui, U Bx, FR
D. Archambault, UBC, CA
T. Munzner, UBC, CA
@labri.fr