HCC class lecture 23 comments

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HCC classlecture 23 comments
John Canny4/18/05
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Administrivia

• Reminder Project presentations on May 9 and 11.

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Role and Position

• Role is an intuitive idea it is what the actor
  does in the network.
• People with similar roles should be
  interchangeable in the network, so role analysis
  is similar to paradigmatic analysis from
  semiotics.

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Role and Position

• Position is an explicit set of similar actors.
  These actors share the same set of relations with
  others.
• Role is the pattern of relations between the
  actors.
• Therefore role is the more abstract, portable
  notion. E.g. Mother, child, manager, travel
  agent, can be defined by particular sets of
  relations between these actors and certain other.
  
• The position of father in a particular network is
  the set of actors who act as fathers to others in
  the network.

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Equivalence

• Regular equivalence Actors are equivalent if
  they have ties to others with the corresponding
  roles.
• e.g. A has the role of mother because of ties to
  B, C, D, who have the role of son or
  daughter.

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Equivalence

• Regular equivalence Actors are equivalent if
  they have ties to others with the corresponding
  roles.
• e.g. A has the role of mother because of ties to
  B, C, D, who have the role of son or
  daughter.

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Equivalence

• Structural equivalence is an easy notion to deal
  with, since it depends on the actual identities
  of the neighbors. E.g. correlations or euclidean
  distance comparison can be used.
• Regular equivalence is a more useful idea, but is
  trickier because its definition is recursive One
  must know the neighbors roles before assigning a
  new role.
• Regular equivalence is an active area of
  research, although some solutions exist.

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Hierarchical clustering

• One natural way to build a regular equivalence
  relation is to hierarchically cluster the data
• Actors are clustered together if they have the
  similar relations to other actors (structural
  equivalence).
• Then we repeat the clustering on the abstracted
  graph (actors are clusters from the previous
  step), etc
• In this way, neighbors are labeled with roles
  from the previous step.

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Discussion Topics

• T1 How do role and position relate to
  communities of practice? Are such communities
  actually positions in a network, or do they
  have internal roles, or both?
• T2 The readings argue that its often helpful to
  use typed ties (e.g. a tie that is explicitly
  labeled mother). By using example networks that
  you know, critique this idea. Can ties always be
  typed? Or are there ties whose type may not be
  known a priori?