February 21st, 2012 Dagstuhl seminar "Information visualization, visual data mining and machine learning", Schloss Dagstuhl, Germany

1. Clustered graph, visualization, hierarchical
visualization
Nathalie Villa-Vialaneix
http://www.nathalievilla.org
SAMM (Université Paris 1)
2012/02/21 - Dagstuhl seminar 12081
Dagstuhl Seminar 12081 (2012/02/21) Graph visualization & clustering Nathalie Villa-Vialaneix 1 / 4

2. Full vs simplified visualization
Framework: Static graph visualization.
Standard (FDP) approach: visualize the whole graph
aims at being aesthetic ⇒ tends to place the hubs in the center of the
figure (edges with uniform length); does not emphasize dense groups
Dagstuhl Seminar 12081 (2012/02/21) Graph visualization & clustering Nathalie Villa-Vialaneix 2 / 4

3. Full vs simplified visualization
Framework: Static graph visualization.
Simplified approach: find communities and represent each one by a
glyph
Dagstuhl Seminar 12081 (2012/02/21) Graph visualization & clustering Nathalie Villa-Vialaneix 2 / 4

4. Full vs simplified visualization
Framework: Static graph visualization.
Simplified approach: find communities and represent each one by a
glyph and investigate sub-structure by a hierarchical clustering
Dagstuhl Seminar 12081 (2012/02/21) Graph visualization & clustering Nathalie Villa-Vialaneix 2 / 4

5. Basic description
1 Search for communities: node clustering (e.g., modularity
optimization)
Dagstuhl Seminar 12081 (2012/02/21) Graph visualization & clustering Nathalie Villa-Vialaneix 3 / 4

6. Basic description
1 Search for communities: node clustering (e.g., modularity
optimization)
Is the clustering relevant / significant?
Dagstuhl Seminar 12081 (2012/02/21) Graph visualization & clustering Nathalie Villa-Vialaneix 3 / 4

7. Basic description
1 Search for communities: node clustering (e.g., modularity
optimization)
Is the clustering relevant / significant?
Possible answer: generate N random graphs with the same degree
distribution and compare the observed optimal modularity to the
optimal modularity distribution among the N random graphs
Dagstuhl Seminar 12081 (2012/02/21) Graph visualization & clustering Nathalie Villa-Vialaneix 3 / 4

8. Basic description
1 Search for communities: node clustering (e.g., modularity
optimization)
2 Iterate the clustering in each class in a hierarchical way.
When to stop the process? Is the clustering relevant /
significant?
Dagstuhl Seminar 12081 (2012/02/21) Graph visualization & clustering Nathalie Villa-Vialaneix 3 / 4

9. Basic description
1 Search for communities: node clustering (e.g., modularity
optimization)
2 Iterate the clustering in each class in a hierarchical way.
3 Visualize the graph (in a simplified way) at various levels of the
clustering hierarchy.
Dagstuhl Seminar 12081 (2012/02/21) Graph visualization & clustering Nathalie Villa-Vialaneix 3 / 4

10. Basic description
1 Search for communities: node clustering (e.g., modularity
optimization)
2 Iterate the clustering in each class in a hierarchical way.
3 Visualize the graph (in a simplified way) at various levels of the
clustering hierarchy.
How to have consistent representations? (a cluster and its
subclusters are approximately displayed at the same place) How to
take into account the space needed for a cluster of the last level of the
hierarchy in any representation (at any level)?
Dagstuhl Seminar 12081 (2012/02/21) Graph visualization & clustering Nathalie Villa-Vialaneix 3 / 4

11. Basic description
1 Search for communities: node clustering (e.g., modularity
optimization)
2 Iterate the clustering in each class in a hierarchical way.
3 Visualize the graph (in a simplified way) at various levels of the
clustering hierarchy.
How to have consistent representations? (a cluster and its
subclusters are approximately displayed at the same place) How to
take into account the space needed for a cluster of the last level of the
hierarchy in any representation (at any level)?
Possible solution: Recursively estimate the place needed for each
cluster in the hierarchy (by a circle encompassing the visualization of
all sub-clusters) ⇒ over-estimation
Dagstuhl Seminar 12081 (2012/02/21) Graph visualization & clustering Nathalie Villa-Vialaneix 3 / 4

12. Basic description
1 Search for communities: node clustering (e.g., modularity
optimization)
2 Iterate the clustering in each class in a hierarchical way.
3 Visualize the graph (in a simplified way) at various levels of the
clustering hierarchy.
Include information about the quality of the clustering in the
representation? (user warning)
Example: Color and weight edges
between clusters according to their
contribution to the modularity
Dagstuhl Seminar 12081 (2012/02/21) Graph visualization & clustering Nathalie Villa-Vialaneix 3 / 4

13. Open issues
• Clustering: what is a meaningful clustering? When to stop the
hierarchy?
• Clustering hierarchy representation: how to anticipate, at a given
level, the place needed for the representation of the finest levels?
• Including estimation about the clustering quality in the
representation: at the node level (“quality” of the clustering for the
cluster? What does that mean?) or at the edge level (contribution to
the modularity between clusters?)
Dagstuhl Seminar 12081 (2012/02/21) Graph visualization & clustering Nathalie Villa-Vialaneix 4 / 4