1. Community Detection  Definition: Community Detection  Girwan Newman Approach  Hierarchical Clustering

2. Community Detection

3. Community Detection: Girvan Newman Approach

4. Girwan Newman Approach: Modularity

5. Variations of Girwan Newman Algorithm

6. Hierarchical Clustering Algorithms Important: 1.Clustering obtained by cutting the dendo-gram at a desired level. 2.Each connected component forms a cluster. 3.Basically we use some similarity threshold to get the clusters of desired quality.

7. Hierarchical Clustering Algorithms

8. Variations of Agglomerative clustering-1

9. Variations of Agglomerative clustering-2

10. Variations of Agglomerative clustering-3

11. Strength & Weaknesses Strengths of Hierarchical Clustering: Do not require information regarding number of clusters. Any desired number of clusters can be obtained by ‘cutting’ the dendogram at the proper level. Weaknesses: Not efficient -- the complexity is O(n^2). Once a decision is made to combine two clusters, it cannot be undone. No objective function is directly minimized.

12. Pseudo code – Agglomerative Clustering Source: Walter et. al.; Fast Agglomerative Clustering for Rendering

13. Pseudo code Pseudo code for Agglomerative Clustering, based on KD-Tree

14. References P.-N. Tan, M. Steinbach, and V. Kumar, editors. "Introduction to Data Mining." Pearson Addison Wesley, 2005. B. Walter, K. Bala, M. Kulkarni, and K. Pingali. "Fast Agglomerative Clustering for Rendering." IEEE Symposium on Interactive Ray Tracing, 2008. Girvan M. and Newman M. E. J., Community structure in social and biological networks, Proc. Natl. Acad. Sci. USA 99, 7821– 7826 (2002) Andrea Lancichinetti and Santo Fortunato (2011). "Limits of modularity maximization in community detection". Physical Review E 84: 066122. arXiv:1107.1155 Survey article Communities in Networks (Notices of the American Mathematical Society.