Dynamics of Galois Lattices The case of epistemic communities

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Dynamics of Galois LatticesThe case of epistemic
communities
Camille Roth Paul Bourgine roth,bourgine_at_shs.
polytechnique.fr CREA Centre de Recherche in
Applied EpistemologyCNRS / Ecole Polytechnique -
Paris, France.
Sunbelt XXV, Redondo Beach, CA, USA - Feb 16-20th
2005
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ObjectiveEpistemic community taxonomy/dynamics

• Describe communities of knowledge, in particular
  scientific communities, and their taxonomy e.g.
  trends/subfields within a paradigm.
• Epistemic community group of agents who share
  a common set of topics, concerns, problems who
  share a common goal of knowledge creation.
• (Haas (1992), Cowan et al. (2000), Dupouet et al.
  (2001)).
• Definition used here  an epistemic community
  is the largest set of agents that share a given
  concept set

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Formal frameworkDefinitions
Epistemic community taxonomy/dynamics

• Consider the bipartite graph on R
• Intent of an agent set S all concepts used by
  every agent in S
• Epistemic group pair (S, C), where C is the
  intent of S.
• Epistemic community (based on a concept set C)
  the maximal epistemic group based on C.
• Dual notions
• examples (A,B,C,E, McB)
• (B,C, McB,EmG)

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Formal frameworkGalois lattice
Epistemic community taxonomy/dynamics

• Good news the extent of the intent of an agent
  set yields its epistemic community.
• e.g. from C,D, whose intent is EmG, whose
  extent is B,C,D, we get ? (B,C,D, EmG)
  epistemic community
• Pb there may be many such communities

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Formal frameworkGalois lattice
Epistemic community taxonomy/dynamics
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CategorizationGalois lattice
Epistemic community taxonomy/dynamics

• Hypotheses on scientific communities they are
  structured (i) into fields, with common concerns,
  and (ii) hierarchically, through
  generalization/specialization relations.
• We need a categorization method that allows
  overlap.
• The Galois lattice is the ordered set of all
  epistemic communities (closed couples), provided
  with the natural partial order on sets.

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CategorizationGalois lattice
Epistemic community taxonomy/dynamics
 basic-level 
more general more specific
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Galois latticeClosed couple relevance
empirical results
Epistemic community taxonomy/dynamics

• Try to find a relevant level of
  generality/precision for the closed sets so that
  the lattice is manageable.
• Given the assumptions, first criterion fields
  agent set size.
• Very poor linguistic assumptions small
  stop-word list, basic lemmatization, no
  contextual processing, no homonymy, synonymy,
  syllepsis, nominal groups
• Computation of the lattice for a relation from
  MedLine data on zebrafish, 1990-1995 (6 years).

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Galois latticeEmpirical results
Epistemic community taxonomy/dynamics
Galois lattice on  zebrafish  community
density of closed sets against extension sizes
(author sets) as a proportion of agents of the
whole community (200 authors) (1800 concepts)
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Galois latticeEmpirical results
Epistemic community taxonomy/dynamics

• Large ECs remarkable stylized fact of the data.
• Partial real lattice successfully checked by
  domain experts

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Galois latticeSelection
Epistemic community taxonomy/dynamics

• -gt Improve selection criteria, since agent set
  size is
• Over-selective Large yet less significant sets.
• Additional criterion Ratio between set and
  superset sizes.
• (2) Under-selective Small yet significant sets.
• Additional criterion Distance from the top.

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Galois latticeSelection and dynamics
Epistemic community taxonomy/dynamics

• Three 6-year periods 90-95, 94-99 and 98-03.
  Selection on 70 words.
• Booming community from 1000 authors at the end
  of 1995, to 9700 by 2004 (and 3700 in 1999).
• Selection criteria
• (1) catch large communities Size/distance
  attributes
• (2) catch isolated communities Size/distance
  number of sons

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DynamicPartialLattice
Epistemic community taxonomy/dynamics
90-95
98-03
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thanks
to be continued on http//camille.roth.free.fr
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extra stuff
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Formal frameworkDefinitions
Objective 1 - Epistemic community
taxonomy/dynamics

• More formally for X ? S, Y ? C,
• Properties
• and as such, it is a closure operation. X
  is said closed iff XX.
• Closed coupleA closed couple is thus an
  epistemic community.

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Galois latticeEmpirical results
Epistemic community taxonomy/dynamics
Decreasing cumulated frequencies
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Categorization
Epistemic community taxonomy/dynamics

• Many epistemic communities how to categorize ?
• Computer science methods (euclidian distances
  derivates, based more on computational than
  sociological hypotheses)
• Approaches stemming from sociology structural
  balance, blockmodeling, structural cohesion...
• pb 1 few hierarchical methods, and if so,
  mostly trees or dendrograms
• pb 2 they work fine on small sets