Information Technology Reference
In-Depth Information
learning the relational ranking function with Ranking SVM is given in [
6
]. The cor-
responding algorithm is named “
Relational Ranking SVM
(RRSVM)”. The matrix-
form expressions of RRSVM are given as below.
RRSVM for pseudo relevance feedback can be represented as the following op-
timization problem:
n
1
2
1
(i)
T
ξ
(i)
,
2
min
w,ξ
(i)
w
+
λ
i
=
1
C
(i)
h
f
w,
x
(i)
,R
(i)
≥
1
(i)
ξ
(i)
,ξ
(i)
s.t.
−
≥
0
,
(6.5)
h
f
w,
x
(i)
,R
(i)
=
I
β
D
(i)
R
(i)
−
1
f
w,
x
(i)
,
−
−
where
C
(i)
denotes a constraint matrix for query
q
i
,
1
(
i
)
denotes a vector with all
the elements being 1, and its dimension is the same as that of
ξ
(i)
. Each row of
C
(i)
1, and the
other elements are all 0. For example, for query
q
i
, if the ground truth indicates that
y
1
>y
3
and
y
2
>y
4
, then we have
represents a pairwise constraint: one element is 1, one element is
−
10
.
10
01 0
−
C
(i)
=
−
1
RRSVM for topic distillation can be represented as the following optimization
problem:
n
1
2
1
(i)
T
ξ
(i)
,
2
min
w,ξ
(i)
w
+
λ
i
=
1
C
(i)
h
f
w,
x
(i)
,R
(i)
≥
1
(i)
ξ
(i)
,ξ
(i)
s.t.
−
≥
0
,
(6.6)
h
f
w,
x
(i)
,R
(i)
=
2
I
β
2
D
(i)
R
(i)
T
−
1
R
(i)
+
−
−
×
2
f
w,
x
(i)
−
βr
(i)
.
Further discussions indicate that although the ranking function becomes more
complicated, one only needs to pre-process the features of all the documents associ-
ated with a given query, and can still use standard Ranking SVM toolkits to perform
the learning and test.
1
Therefore the new algorithm is very feasible for practical use.
Experimental results in [
6
] have shown that for particular learning tasks, RRSVM
can significantly outperform Ranking SVM and other heuristic methods such as
the pseudo relevance feedback method provided in the Lemur toolkit
2
and sitemap-
based relevance propagation [
5
].
1
For example,
http://olivier.chapelle.cc/primal/
and
http://www.cs.cornell.edu/People/tj/svm_light/
svm_rank.html
.
2
http://www.lemurproject.org/
.
