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BSP Clustering Algorithm for Social Network Analysis

Elektrotehni čki fakultet Univerziteta u Beogradu. BSP Clustering Algorithm for Social Network Analysis. Branislav Petrović 3273/2012. Introduction. Social Networks - highly dynamic, evolving relationships among people or other entities.

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BSP Clustering Algorithm for Social Network Analysis

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  1. Elektrotehnički fakultet Univerziteta u Beogradu BSP Clustering Algorithm forSocial Network Analysis Branislav Petrović 3273/2012

  2. Introduction • Social Networks - highly dynamic, evolving relationships among people or other entities. • Social Network Analysis (SNA) – new research field in data mining. • Research on SNA includes: clustering analysis, classification, link prediction.

  3. Introduction • Traditional clustering algorithms group objects based on their similarity. • Social network clustering analysis divides objects into classes based on their links as well as their attributes.

  4. Social network in graph theory • Social Network - directed graph composed by objects and their relationship.

  5. Business System Planning (BSP) • BSP clustering algorithm uses objects and links among objects to make clustering analysis. • Steps of BSP algorithm: • Generate edge creation matrix and edge pointed matrix • Calculate one-step reachable matrix between objects • Calculate multi-steps reachable matrix between objects • Calculate reachable matrix • Identify relationships among classes

  6. Generate Lc and Lp • Lc – m x n edge creation matrix. • Lp – m x n edge pointed matrix. • Lc (i, j) =1 - object Oi connects with the tail of edge Ej • Lp (i, j) =1 - object Oi connects with the head of edge Ej

  7. Calculate one-step reachable matrix • i = 1..m, j = 1..n. • ^ – Boolean product. • V– Boolean sum. • G(i, j) =1 – Oi to Oj is a one-step reachable relation.

  8. Calculate multi-step reachable matrix • i = 1..m, j = 1..n.

  9. Calculate reachable matrix R=I*VG*VG2 *...*VGm−1 • I – unit matrix. • V – Boolean sum. • R(i, j) = 1 – reachable relation exists from Oi to Oj.

  10. Calculate mutual reachable matrix Q=R^RT • ^ – Boolean product. • Q(i, j) = 1 – there are mutual reachable relation between Oi and Oj . • Strong sub-matrix – all elements in a sub-matrix of Q are 1.

  11. Identify relationships among classes • If there is one-step reachable relation between two objects in different classes, directed links exist between those classes.

  12. Social network clustering analysisalgorithm Input: Lc : Edge creation Matrix Lp : Edge pointed matrix Begin for k=3 to m do Gk −1 =Gk −2 *G R = I V G V G2 ... V Gm−1 Qk− > C (Ck ,Q)->Relation (Ck ) End • Qk− > C – generating clusters • through mutual reachable matrix Q. • (Ck ,Q ) – > Relation(Ck) – identifying relationships among clusters base on clusters and one-step reachable matrix G.

  13. Improvement over BSP Clustering Algorithm • Disadvantage of BSP CA – uses matrices to store edges and reachable relations. • Propose modification – using Link list data structure. Struct snode { Int row, col, val; Struct snode *next; };

  14. Shortcomings • Edges between objects have same weight. • Property of each cluster has not been analyzed.

  15. Thank you for listetning Questions?

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