Elektrotehnički 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.
• Social Network Analysis (SNA) – new
research field in data mining.
• Research on SNA includes: clustering
analysis, classification, link prediction.
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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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Social network in graph theory
• Social Network - directed graph composed
by objects and their relationship.
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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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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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Calculate one-step reachable matrix
G  Lc * Lp
•
•
•
•
n
T
T
 g i , j  V ( l c ( i , k )^ l p ( k , j ))
k 1
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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Calculate multi-step reachable matrix
G  G *G  g
2
m
2
i, j
 V ( g ( i , k )^ g ( k , j ))
k 1
• i = 1..m, j = 1..n.
G  G *G
3
2
G  G *G
4
3
...
G
m 1
G
m2
*G
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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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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 submatrix of Q are 1.
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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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Social network clustering analysis
algorithm
Input:
Lc : Edge creation Matrix
Lp : Edge pointed matrix
Begin
G  Lc * Lp
T
for k=3 to m do
Gk −1 =Gk −2 *G
R = I V G V G2 ... V Gm−1
T
Q  R^ R
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 onestep reachable matrix G.
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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;
};
Row
Col
Val
*next
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Shortcomings
• Edges between objects have same weight.
• Property of each cluster has not been
analyzed.
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Thank you for listetning
Questions?
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