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BSP Clustering Algorithm for Social Network Analysis Elektrotehnički fakultet Univerziteta u Beogradu Branislav Petrović 3273/2012

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2/15 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.

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3/15 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.

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4/15 Social network in graph theory Social Network - directed graph composed by objects and their relationship.

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5/15 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

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6/15 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

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7/15 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.

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8/15 Calculate multi-step reachable matrix i = 1..m, j = 1..n.

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9/15 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.

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10/15 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.

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11/15 Identify relationships among classes If there is one-step reachable relation between two objects in different classes, directed links exist between those classes.

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12/15 Social network clustering analysis algorithm 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.

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13/15 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; }; RowColVal*next

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14/15 Shortcomings Edges between objects have same weight. Property of each cluster has not been analyzed.

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15/15 Thank you for listetning Questions?

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