Diapositive 1

Overwiew & Objectives

	why synonymy?
	what : Conceptual vectors
	which synonymies ?
	for what : Use with lexical functions

Objectives

	Evaluation
		Semantic proxymity to possible contexts for lexical interchangeability
	Relative synonymy
		Elimination of transitivity
		punctum proximum
	Subjective synonymy
		punctum remotum

Conceptual vectors vector space

	An idea
		Concept combination Ñ a vector
	Idea space
		= vector space
	A concept
		= an idea = a vector V
		with augmentation: V + neighboorhood
	Meaning space
		= vector space + {v}*

Conceptual vectors Thesaurus

	H : thesaurus hierarchy Ñ K concepts
		Thesaurus Larousse = 873 concepts
	V(Ci) : <a1, É, ai, É , a873>
		aj = 1/ (2 ** Dum(H, i, j))

Conceptual vectors Concept c4:peace

Conceptual vectors Term ÒpeaceÓ

Angular distance

	DA(x, y)  = angle (x, y)
		0 £ DA(x, y) £ p
		if 0 then x & y colinear Ñ same idea
		if p/2 then nothing in common
		if p then DA(x, -x) with -x  Ñ anti-idea of x

Angular distance

	DA(x, y) = acos(sim(x,y))
	DA(x, y) = acos(x.y/|x||y|))
			DA(x, x) = 0
			DA(x, y) = DA(y, x)
			DA(x, y) + DA(y, z) ³ DA(x, z)
			DA(0, 0) = 0  and  DA(x, 0) = p/2 by definition
			DA(ax, by) = DA(x, y) with ab > 0
			DA(ax, by) = p - DA(x, y) with ab < 0
			DA(x+x, x+y)  = DA(x, x+y) £ DA(x, y)

Thematic distance

	Examples
		DA(tit, tit) = 0
		DA(tit, passerine) = 0.4
		DA(tit, bird) = 0.7
		DA(tit, train) = 1.14
		DA(tit, insect) = 0.62
		tit = insectivorous passerine bird É

Relative synonymy Aspectual or referential

	Term polysemy
			un personnel triŽ sur le volet (CHOISIR)
			une liste triŽe par ordre alphabŽtique (ORDONNER)
			le courrier est triŽ (REPARTIR)
	A vector plays as an aspect (aka reference)
	How can we exchange A & B in the context of C ?

Relative synonymy

	SynR(A, B, C) with  C as a reference (ref)
		SynR(A, B, C) = DA(A+A€C, B+B€C)

Relative synonymy Properties

		SynR(A, B, C) = SynR(B, A, C)
		SynR(A, A, C) = DA(A € C, A € C) = 0
		SynR(A, B, 0) = DA(A, B
		SynR(A, 0, C) =  p/2
		DA(charbon,nuit) = 0.9
		SynR(charbon, nuit, couleur) = 0.4
		SynR(charbon, nuit, noir) = 0.35

Relative synonymy Properties

	The relative synonymy is a measure which favors the closing in of 2 vectors:
			ÒblackÓ a good punctum proximum for ÒcoalÓ and ÒnightÓ
	Transitivity of the synonymy
		SynR(coal, crow, black) = 0.18
		SynR(crow, night, black)                = 0.5
		SynR(coal, night, black) = 0.35

Absolute synonymy

	SynA(A, B) a particular case with  A€B as ref
		SynA(A, B) = SynR (A, B, A€B)

Subjective synonymy Point of view

	Semantic discrimination scope
			DA(tit, bird) = 0.7
			DA(sparrow, bird) = 0.48
			DA(tit, sparrow) = 0.23
	With which pow can we discriminate two given vectors?
			Closest Òpunctum remotumÓ

Subjective synonymy

	SynS(A, B, C) Ñ C = point of view (pow)
	SynS(A, B, C)
	= D(A-A€C, B-B€C)

Subjective synonymy

		When DA(A, C) ¨ p/2 & DA(B, C) ¨ p/2 then SynS(A, B, C) ¨ DA(A,B)
		SynS(A, B, 0) = DA(A, B)
		SynS(A, A, C) = 0
		SynS(A, B, B) = DA(A-A€B, 0)  = p/2
		DA(tit, crow) = 0.32
		SynS(tit, crow, zoology) = 0.54
		SynS(tit, crow, bird) = 1.07
		SynS(tit, crow, passerine) = 1.37

Subjective synonymy Properties

	non conservation of the concept hierarchy chain
		Concept chain
		@the_world > @the_life > @animals > @birds
		DA(tit, sparrow) = 0.23
		SynS(tit, sparrow, @the_life)           = 0.75
		SynS(tit, sparrow, @the_world) = 0.5
		SynS(tit, sparrow, @animals) = 0.4
		SynS(tit, sparrow, @birds) = 0.9
		Concepts horizon (at the lowest concept level)

Subjective synonymy Properties

	Polysemy: term vs concept
		SynS(tit, sparrow, @birds) = 0.9
		SynS(tit, sparrow, bird)             = 0.78
	Loosly correlated vectors as pow
		SynS(tit, sparrow, @gold) =  0.7
		DA(tit, @gold) = 1.19
		DA(sparrow, @gold) = 1.15

Objective synonymy

	SynA(A, B) a particular case with A€B as pow
	SynA(A, B)
	= SynA(A, B, A€B)

Conclusion

	Synonymy as enhancement of the thematic analysis
	The conceptual vector models shows interferencies
		from polysemy : relative synonymy
		from the complex relation btw concept and terms (bird vs @birds)
	System in continuous learning
		Evolving results
		Hopefully converging