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BSP Clustering Algorithm for Social Network Analysis

igor-jacobson avatar
igor-jacobson
15 diapositives · 323 Views · Nov 16, 2014

This paper presents the BSP clustering algorithm tailored for social network analysis. It explores social networks as dynamic graphs consisting of entities and their interconnections. The research elucidates clustering analysis, which divides entities by their relationships and attributes, as opposed to conventional methods based purely on similarity. The BSP algorithm generates edge creation and pointed matrices, calculates reachable matrices, and identifies relationships among classes. With proposed modifications to optimize performance, this work contributes to an evolving field of data mining.

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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?