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


Formal frameworkGalois lattice


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.


CategorizationGalois lattice

« basic-level »

more general

more specific


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).


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



• Large ECs: remarkable stylized fact of the data.

• Partial real lattice successfully checked by domain experts:


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.


Galois latticeSelection and 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


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



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


Dynamics of Galois Lattices The case of epistemic communities Camille Roth & Paul Bourgine {...

Documents

Transcript of Dynamics of Galois Lattices The case of epistemic communities Camille Roth & Paul Bourgine {...