Visual Analytics - Los Alamos National...
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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
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Exploratory Analysisin Networks
Most network analyses try to detecta given type of structure, such as
- Small-world Watts & Strogatz, Nature 393, 440 (1998), ....
- Scale-freeBarabási & Albert, Science 286, 509 (1999), ....
- Community structureNewman & Girvan, PRE 69, 026113 (2004),Porter, Onnela, & Mucha, Notices Amer Math Soc 56, 1082 (2009), ....
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Exploratory Analysisin Networks
• An exploratory analysis tries to discover an unknown structure.Newman & Leicht, PNAS 104, 9564 (2007)
• We take visual analytics approach for this problem.
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Visual Analytics
• Visual interaction between the human user and the analytical tools for analyzing and interpreting high-dimensional complex data
• We take this approach for discovering an unknown group structure among nodes in a network data set.
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Only 5% of links are chosen
randomly and shown.
DegreeNeighbor’s mean degree2nd neighbor’s mean degreeClustering coefficient
Discovering Unknown Group Structures
Betweenness centralityLaplacian eigenvectorsNormalized Laplacian eigenvectorsMean shortest path
Distinct groups?
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How it works: Random 2D Projection
Only 5% of links are chosen
randomly and shown.
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Reject Divide
How it works:Visual Interactions
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How it works:Patterns of User Inputs
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How it works:Grouping Binary Patterns
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= the number of nodes in group k
Properties Discriminating Nodes
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
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Example 2Community Structure
Text
pwithin = 0.3pacross = 0.03
0.3
0.03 0.03
0.3 0.30.03
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Example 3Mixed Group Structure
0.01
0.01
0.2
0.020.01
0.01
0.01 0.010.2
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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
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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
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Example 4: PACS Network
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A problem with k-Means Clustering
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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, ...
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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?