Synonymies and conceptual vectors

NLPRS 2001

Mathieu Lafourcade, Violaine PrinceLIRMM - France

Overwiew & Objectives

why synonymy?

what : Conceptual vectors

which synonymies ?

for what : Use with lexical functions

• Evaluation• Semantic proxymity to possible contexts

for lexical interchangeability

• Relative synonymy• Elimination of transitivity

punctum proximum

• Subjective synonymypunctum remotum

Objectives

Conceptual vectorsvector space

• An ideaConcept combination — 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 — K conceptsThesaurus Larousse = 873 concepts

• V(Ci) : <a1, …, ai, … , a873>

aj = 1/ (2 ** Dum(H, i, j))

1/41 1/41/41/161/16 1/64 1/64

2 64

Conceptual vectors Concept c4:peace

peace

hiérarchical relations

conflict relations

The world, manhood society

Conceptual vectors Term “peace”

c4:peace

Angular distance

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

x’

y

x

Angular distanceDA(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) DA(x, z)

DA(0, 0) = 0 and DA(x, 0) = /2 by definition

DA(x, y) = DA(x, y) with 0

DA(x, y) = - DA(x, y) with < 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 …

Relative synonymyAspectual or referential

• Term polysemy

• un personnel trié sur le volet (CHOISIR)• une liste triée par ordre alphabétique (ORDONNER)• le courrier est trié (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+AC, B+BC)

B

A

C

A+AC

B+BC

SynR(A, B, C)

Relative synonymyProperties

• 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) = /2

• DA(charbon,nuit) = 0.9

• SynR(charbon, nuit, couleur) = 0.4

• SynR(charbon, nuit, noir) = 0.35

Relative synonymyProperties

• The relative synonymy is a measure which favors the closing in of 2 vectors:

“black” a good punctum proximum for “coal” and “night”

• 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 AB as ref

SynA(A, B) = SynR (A, B, AB)

B

A

AB

A+AAB)

B+B(AB)

SynA(A, B)

Subjective synonymyPoint 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 “punctum remotum”

Subjective synonymy

• SynS(A, B, C) — C = point of view (pow)

SynS(A, B, C)

= D(A-AC, B-BC)

B

A

C

A-AC

B-BC

SynS(A, B, C)

Subjective synonymyWhen DA(A, C) /2 & DA(B, C) /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-AB, 0) = /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 synonymyProperties

• non conservation of the concept hierarchy chainConcept 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 synonymyProperties

• 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 AB as pow

SynA(A, B)

= SynA(A, B, AB)

B

A A-A(AB)

B-B(AB)

SynA(A, B)

AB

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