Information Technology Reference
In-Depth Information
Fig. 2.3
Learning process of
PRanking
Fig. 2.4
Fixed-margin
strategy
2.4.2 Ranking with Large Margin Principles
Shashua and Levin [
20
] try to use the SVM technology to learn the model parameter
w
and thresholds
b
k
(k
1
,...,K)
for ordinal regression.
Specifically, two strategies are investigated. The first one is referred to as the
fixed-margin strategy
.
Given
n
training queries
=
x
(i)
j
m
(i)
j
n
i
1
, their associated documents
x
(i)
{
q
i
}
={
}
1
,
=
=
y
(i)
j
m
(i)
j
=
and the corresponding relevance judgments
y
(i)
1
, the learning process
is defined below, where the adoption of a linear scoring function is assumed. The
constraints basically require every document to be correctly classified into its target
ordered category, i.e., for documents in category
k
,
w
T
x
(i
j
should exceed threshold
b
k
−
1
but be smaller than threshold
b
k
, with certain soft margins (i.e., 1
={
}
−
ξ
(i)
∗
j,k
1
and
−
−
ξ
(i)
1
2
controls the complexity of the
1
j,k
), respectively (see Fig.
2.4
). The term
2
w
model
w
.
