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/
.