Transcript Social Position & Social Roles

Social Position & Social Role
Lei Tang
2009/02/13
Social Postion
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Position: A collection of individuals who are similarly
embedded in networks of relations.
Position is different from cluster (or cohesive subgroup)
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Group is formed based on adjacency, proximity or reachability
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This is typically adopted in current data mining.
Position is based on the similarity of ties among subsets of
actors.
Actors occupying the same position need not be in direct, or
even indirect contact with each other.
Social Role
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Roles: the patterns of relations which obtain between actors of
between positions
Position focuses on actors while roles focus on relations
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E.g. Kinship role defined as combination of marriage and descent.
Can be modeled in three levels:
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Actors
Subsets of actors
The whole network
Based on multiple relations and the combinations of these relations
Overview of Positional & Role Analysis
Multirelational
Data
Group Relations
(Individual level)
Group actors
Usual Positional
Analysis
Usual Role
Analysis
Group actors
Group Relations
(group level)
Roles and
Positions
Structural Equivalence
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Actor I and J are structurally equivalent:
 For all the other actors k (!=I or J), actor I has tie to k iff actor J has
tie to k.
Sociamatrix
2
1
Example:
1 2 3 4 5
1 - 0 1 1 0
4
3
2 0 - 1 1 0
3 0 0 - 0 1
4 0 0 0 - 1
5
5 0 0 0 0 -
The submatrices corresponding to the ties between and within
positions are filled with either all 0’s or all 1’s.
Positional Analysis
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Major objective: simplify the information in a network
data set
Tasks:
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A formal definition of equivalence
A measure of equivalence
A representation of equivalence
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Density matrix
Image matrix
Reduced graph
Asses adequacy (Goodness of fit)
Structural equivalence to Valued Ties
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For discrete ties, easy to define structural equivalence.
(Very strict)
For valued ties
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Euclidean distance
Correlation
Partition Actors (Clustering)
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Consider each row as one data instance.
 Agglomerative Hierarchical clustering
 CONCOR (convergence of iterated correlations)
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Based on multirelaitonal network A,
Calculate pairwise correlation matrix C1
Compute pairwise correlation matrix C2 based on C1.
Continue until we get the block of +1/-1
+1 -1
-1
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+1
CONCOR is connected to PCA. (the top eigenvector)
Can only split into two positions, like divisive clustering
Role Analysis
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Consider different combination of relations
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E.g. if aRb denotes a is mother of b, then
aRRb represent a new relation (grandmother)
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They assume the relations between actors are already known.
But for us, this is seldom known.
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The book is focusing more on analysis rather than methodology
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