Visual Analytics for discovering group structures in networks Takashi Nishikawa 1,2 Adilson E. Motter 2,3 1 Department of Mathematics, Clarkson University 2 Department of Physics & Astronomy, Northwestern University 3 Northwestern Institute on Complex Systems (NICO), Northwestern University LANL seminar March 16, 2010 Funded by NSF
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Visual Analytics for discovering group structures
in networksTakashi Nishikawa1,2
Adilson E. Motter2,3
1Department of Mathematics, Clarkson University2Department of Physics & Astronomy, Northwestern University
3Northwestern Institute on Complex Systems (NICO), Northwestern University
LANL seminar March 16, 2010
Funded by NSF
Exploratory Analysisin Networks
Most network analyses try to detecta given type of structure, such as
We choose node properties with largest Dj, and project points onto the corresponding subspace.
Gk: set of indices for nodes in group k
For node property j, define
Example 2Community Structure
Text
pwithin = 0.3pacross = 0.03
0.3
0.03 0.03
0.3 0.30.03
Example 3Mixed Group Structure
0.01
0.01
0.2
0.020.01
0.01
0.01 0.010.2
Example 4: PACS Network
89.75 05.45Nodes are connected if there are more papers than expected by random & independent occurrenceComplex systems
Nonlinear dynamics and chaos
Data source: http://www.atsweb.neu.edu/ngulbahce/pacsdata.htmlReference: M. Herrera, D.C. Roberts and N. Gulbahce, arxiv:0904.1234
Example 4: PACS Network
Example 4: PACS Network
A problem with k-Means Clustering
Future Work
Comprehensive benchmarking
• As a network group detection method: against community detection algorithms, expectation-maximization method, ...
• As a high-dimensional clustering method: against k-means clustering, unsupervised SVM, ...
Future Work
• Can we substitute human eye with 2-means clustering or unsupervised two-class SVM?
• Exploring a high-dimensional network parameter space, given only coarse & non-uniform sample points: How does dynamical properties (cascading, synchronization, etc.) depend on network structural parameters?