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s
f
s
s
a
b
x
x
s =
1
2
s
b
t
t
t
a
f
b
y
y
t =
1
2
t'
b
Fig. 3.2.
Sentence segments.
rK
(
s, t
)=
fbK
(
s, t
) +
bK
(
s, t
) +
baK
(
s, t
) +
mK
(
s, t
)
bK
i
(
s, t
)=
K
i
(
s
b
,t
b
,
1)
· c
(
x
1
,y
1
)
· c
(
x
2
,y
2
)
· λ
l
(
s
b
)+
l
(
t
b
)
fbK
(
s, t
)=
i,j
bK
i
(
s, t
)
· K
j
(
s
f
,t
f
)
,
1
≤
i
,
1
≤
j
,
i+j
<
fb
max
bK
(
s, t
)=
i
bK
i
(
s, t
)
,
1
≤
i
≤
b
max
baK
(
s, t
)=
i,j
bK
i
(
s, t
)
· K
j
(
s
a
,t
a
)
,
1
≤
i
,
1
≤
j
,
i+j
<
ba
max
mK
(
s, t
)=
1
(
s
b
=
∅
)
·
1
(
t
b
=
∅
)
· c
(
x
1
,y
1
)
· c
(
x
2
,y
2
)
· λ
2+2
,
Fig. 3.3.
Computation ofrelationkernel.
common counts arecalculated separatelyin
bK
i
, whichis definedas the number of
common subsequences of length
i
between
s
b
and
t
b
, anchoredat
x
1
/
x
2
and
y
1
/
y
2
respectively (i.e., constrainedtostart at
x
1
in
s
b
and
y
1
in
t
b
, and toend at
x
2
in
s
b
and
y
2
in
t
b
). Then
fbK
simply counts the number of subsequences that match
j
positions before thefirst entity and
i
positions betweentheentities, constrained
to havelength less than a constant
fb
max
. Toobtain a similar formulafor
baK
we
simplyuse the reversed (mirror) version of segments
s
a
and
t
a
(e.g.,
s
a
and
t
a
). In
Section3.2.1weobserved that all three subsequence patterns use at most4words
toexpress arelation, therefore theconstants
fb
max
,
b
max
and
ba
max
aresetto 4.
Kernels
K
and
K
arecomputedusing the procedure describedinSection3.2.2.
3.3 A Dependency-Path Kernel for Relation Extraction
The pattern examples fromSection3.2.1 showthe twoentity mentions, together
with theset ofwords that are relevant fortheir relationship. A closer analysisof
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