1 / 37

Modularity Maximization: Model-Based Detection in Networks

Learn about the popular technique of modularity maximization for detecting community structure in networks. Explore the modularity function, greedy algorithms, spectral methods, and hybrid techniques. Discover the resolution limit and the potential of hybrid detection. Evaluate the method for finding communities and learn about hierarchy community detection. Recommended for those interested in network analysis and community detection.

lstokes
Download Presentation

Modularity Maximization: Model-Based Detection in Networks

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lecture 6-2 Modularity Maximization • Ding-Zhu Du • University of Texas at Dallas lidong.wu@utdallas.edu

  2. Model-Based Detections • Connection-based detection • Modularity maximization • Influence-based detection • Overlapping community detection • Hierarchy community detection

  3. Model-Based Detection Modularity Maximization Is the most popular one

  4. Outline • Modularity Function • Greedy • Spectral Method and MP • Hybrid Method

  5. Modularity Function (Newman 2006)

  6. Modularity Function (Newman 2006)

  7. Newman 2006 • M.E. J. Newman: Modularity and community structure in networks, Proceedings of the National Academy of Sciences, vol 103 no 23 (2006) pp. 8577-8582.

  8. Modularity Function

  9. Modularity Function (Newman 2006)

  10. Modularity Function (digraph)

  11. Why call Modularity? • Module = community in some complex networks • The function describes the quality of modules.

  12. Modularity Max is NP-hard • U. Brandes, D. Delling, M. Gaertler, R. Gorke, M. Hoefer, Z. Nikoloski, and D. Wagner: On modularity clustering, IEEE Transactions on Knowledge and Data Engineering (TKDE), vol 20, no 2 (2008) pp 172-188

  13. Outline • Modularity Function • Greedy • Spectral Method • Hybrid Method

  14. Increment

  15. Greedy Algorithm

  16. Outline • Modularity Function • Greedy • Spectral Method and MP • Hybrid Method

  17. Qualified Cut Community Partition

  18. Quadratic Form

  19. Spectral Method

  20. Linear Program

  21. Vector Program Semi-definite Program

  22. Outline • Modularity Function • Greedy • Spectral Method and MP • Hybrid Method

  23. Resolution limit • Misidentification: some derived communities do not satisfy the weak community definition or even the most weak community definition • In other words, obtained communities may have sparser connection within them than between them.

  24. Hybrid Detection: a Possible Research Direction

  25. Max Q s.t. condition (1) • This may give an improvement. • Is it possible to do? • (1) can be written as linear constraints • Q can be written as a quadratic function • Thus, Max Q s.t. (1) can be formulated as a quadratic programming, which can be transformed into a semi-definite programming

  26. Linear Constraints

  27. Linear Constraints

  28. Modularity Density Modularity Density function (Li et al. 2008)

  29. Opt D s.t. condition (1) • This may give an improvement. • Is it possible to do? • (1) can be written as linear constraints • Q can be written as a fractional function • Thus, Max D s.t. (1) can be formulated as a Geometric Programming.

  30. Outline • Community Structure • Connection-Based Detection • Influence-Based Detection • Remarks

  31. Remark 1 How to evaluate the method for finding a community?

  32. Clustering

  33. Community Detection

  34. Remark 2 How to do hierarchy community detection?

  35. Survey • Introductory review: Communities in networks by M. A. Porter, J.-P. Onnela, and P. J. Mucha, Notices of the American Mathematical Society 56, 1082 (2009) • Comprehensive review: Community detection in graphsby Santo Fortunato, Physics Reports 486, 75 (2010)

  36. THANK YOU!

More Related