1. Lens effects in autonomous terminology and conceptual vector learning
Mathieu Lafourcade
LIRMM - France 1

2. Overwiew & Objectives lexical semantic representations
conceptual vector model (cvm)
autonomous learning by the system
from a given « semantic space » (ontology)
effects of swithing ontologies (general  spec)
global effects on the lexicon
local effects on particular word
ambiguity as noise
towards self contained WSD annotations
« I made a deposit at the bank »
 « I made a deposit at the bank<g:money> »

3. 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

4. 2D view of « meaning space »
“product”
“cat”

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
hierarchical relations
The world, manhood
society

7. Conceptual vectors Term “peace”
c4:peace

8. exchange
profit
finance

9. 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

10. 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

11. 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

12. Some vector operations
Addition : Z = X  Y
zi = xi + yi vector Z is normalized
Term to term mult : Z = X  Y
zi = (xi * yi)1/2
vector Z is not normalized
Weak contextualization : Z = X  (X  Y) = (X,Y)
“Z is X augmented by its mutual information with Y”

13. 2D view of weak contextualization
XY
X(XY)    X
XY
Y(XY)
XY Y

14. Autonomous learning 1/2 set of known words K, set of unknow words U
revise a word w of K OR (try to) learn a word w of U
From the web : for w ask for a def D
specific sites : dicts, synonyms list, etc.  def analysis
general sites : google, etc.  corpus analysis
for each word wd of D
if not in K then add wd to U AND add VO to V*
otherwise get the vector of wd AND add V(wd) to V*
compute the new vector of w from def(D) and V*
98870 words for senses (vectors) learned in 3 years
French
« forever » looping process

15. Autonomous learning 2/2 insectivorous passerine bird … Weighted sum
TXT
Weighted sum
(X,Y) V PH V
N, GOV … V … V
ADJ, …
insectivorous passerine bird … V

16. Local expansion of vector space
“product”
“cat” cn c1 GS G
finer mesh
locally over the space

17. Point of G without link in S
Folding and unfolding S
Specialized ontology
+ a
+ b
General ontology
+ b G
+ c
Point of G without link in S vG … a b … c a …
a+b … b …
b+c … vS
GGS(vG) = vGS
2000
873
GSG(vGS) = vG

18. Local lexical density given a point P
count the number of points at distance d1, d2, dn P
0 ≤ d1 < d2 <…dn ≤ π/2

19. Lexical Distribution from Local density
medium density
curve top centered
high density
curve shifted on the left
low density case left as an exercise

20. Macro level Local density variationG GS

21. Micro level Distance variation
small angle
= high similarity
larger angle
= less similarity G GS

22. Last words Switching of representation global and local test functions
coarse grained to fine grained  better semantic discrimation
… and vice-versa  conservation of resource
global and local test functions
for vector quality assessment
decision taking about level of representation
detectors when combined to lexical functions (antonymy, etc.)
the basis for
self adjustement toward a vector space of constant density
wsd as a reduction of noise (in context or out of context)
unification of ontologies
self emergent structuration of terminology