Dynamics of Galois Lattices The case of epistemic communities Camille Roth & Paul Bourgine {...
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Transcript of Dynamics of Galois Lattices The case of epistemic communities Camille Roth & Paul Bourgine {...
Dynamics of Galois LatticesThe case of epistemic communities
Camille Roth & Paul Bourgine
{roth,bourgine}@shs.polytechnique.fr
CREA Centre de Recherche in Applied EpistemologyCNRS / Ecole Polytechnique - Paris, France.
Sunbelt XXV, Redondo Beach, CA, USA - Feb 16-20th 2005
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»
Formal frameworkDefinitions
• 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})
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…
Formal frameworkGalois lattice
Epistemic community taxonomy/dynamics
Formal frameworkGalois lattice
Epistemic community taxonomy/dynamics
CategorizationGalois lattice
• 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.
Epistemic community taxonomy/dynamics
CategorizationGalois lattice
« basic-level »
more general
more specific
Epistemic community taxonomy/dynamics
Galois latticeClosed couple relevance & empirical results
• 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).
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)
Galois latticeEmpirical results
Epistemic community taxonomy/dynamics
Galois latticeEmpirical results
• Large ECs: remarkable stylized fact of the data.
• Partial real lattice successfully checked by domain experts:
Epistemic community taxonomy/dynamics
Galois latticeSelection
-> Improve selection criteria, since “agent set size” is:
(1) 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.
Epistemic community taxonomy/dynamics
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
DynamicPartialLattice
90-95
98-03
Epistemic community taxonomy/dynamics
thanks…
to be continued on http://camille.roth.free.fr
extra stuff
Formal frameworkDefinitions
• More formally: for X S, Y C,
• Properties:
• “°*”:and as such, it is a closure operation. X is said closed iff X°*=X.
• Closed couple:
A closed couple is thus an epistemic community.
€
X° = y ∈ B |∀x ∈ X,xRy{ }
€
Y* = x ∈ A |∀y ∈ Y,xRy{ }
€
X ⊆ X '⇒ X '° ⊆ X°
€
(X°*)°* = X°*
€
X ⊆ X '⇒ X°* ⊆ X '°*€
X∪X '( )° = X°∩ X '°
€
X ⊆ X°*
€
∀X ⊆ A,Y ⊆B,(X,Y ) complete iff Y=X° and X=Y*
Objective #1 - Epistemic community taxonomy/dynamics
Decreasing cumulated frequencies
Galois latticeEmpirical results
Epistemic community taxonomy/dynamics
Categorization
• 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
Epistemic community taxonomy/dynamics