1. Synonymies and conceptual vectors
NLPRS 2001
Mathieu Lafourcade, Violaine Prince
LIRMM - France 1

2. Overwiew & Objectives why synonymy? what : Conceptual vectors
which synonymies ?
for what : Use with lexical functions

3. Objectives Evaluation Relative synonymy Subjective synonymy
Semantic proxymity to possible contexts for lexical interchangeability
Relative synonymy
Elimination of transitivity
punctum proximum
Subjective synonymy
punctum remotum 2

4. Conceptual vectors vector space
An idea
Concept combination — a vector
Idea space
= vector space
A concept
= an idea = a vector V
with augmentation: V + neighboorhood
Meaning space
= vector space + {v}*  27

5. Conceptual vectors Thesaurus
H : thesaurus hierarchy — K concepts
Thesaurus Larousse = 873 concepts
V(Ci) : <a1, …, ai, … , a873>
aj = 1/ (2 ** Dum(H, i, j))
1/16
1/16
1/4 1
1/4
1/4
1/64
1/64 4 2 6 93

6. Conceptual vectors Concept c4:peace
conflict relations
hiérarchical relations
The world, manhood
society

7. Conceptual vectors Term “peace”
c4:peace

8. 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’ x  y 36

9. 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)  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) 37

10. 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 … 43

11. Relative synonymy Aspectual 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 ? 43

12. SynR(A, B, C) = DA(A+AC, B+BC)
Relative synonymy
SynR(A, B, C) with C as a reference (ref)
SynR(A, B, C) = DA(A+AC, B+BC)
A+AC
SynR(A, B, C) A
B+BC C B 66

13. 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) = /2
DA(charbon,nuit) = 0.9
SynR(charbon, nuit, couleur) = 0.4
SynR(charbon, nuit, noir) = 0.35 67

14. Relative synonymy Properties
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 67

15. SynA(A, B) = SynR (A, B, AB)
Absolute synonymy
SynA(A, B) a particular case with AB as ref
SynA(A, B) = SynR (A, B, AB)
A+A(AB)
SynA(A, B) A
AB
B+B(AB) B 66

16. 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 “punctum remotum” 66

17. Subjective synonymy SynS(A, B, C) — C = point of view (pow)
= D(A-AC, B-BC) A
A-AC C B
SynS(A, B, C)
B-BC 66

18. Subjective synonymy
When 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-AB, 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 66

19. Subjective synonymy Properties
non conservation of the concept hierarchy chain
Concept chain
@the_world
DA(tit, sparrow) = 0.23
SynS(tit, = 0.75
SynS(tit, = 0.5
SynS(tit, = 0.4
SynS(tit, = 0.9
Concepts horizon (at the lowest concept level) 66

20. Subjective synonymy Properties
Polysemy: term vs concept
SynS(tit, = 0.9
SynS(tit, sparrow, bird) = 0.78
Loosly correlated vectors as pow
SynS(tit, = 0.7
= 1.19
= 1.15 66

21. Objective synonymy SynA(A, B) a particular case with AB as pow
= SynA(A, B, AB)
A-A(AB) A
AB B
B-B(AB)
SynA(A, B) 66

22. 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
System in continuous learning
Evolving results
Hopefully converging
107