Information Technology Reference
In-Depth Information
tive frequency, relative frequency in all documents, and inverse document frequency.
The derived model has been tested on typical Cranfield data collections and proven
to be significantly better than a conventional vector space model.
2.3.2 Multi-class Classification for Ranking
Boosting Tree-Based Method
Li et al. [
15
] propose using multi-class classifica-
tion to solve the problem of ranking.
Given documents
x
m
j
={
x
j
}
associated with query
q
, and their relevance judg-
=
1
m
j
ment
y
={
y
j
}
1
, suppose we have a multi-class classifier, which makes prediction
=
y
j
on
x
j
. Then the loss function used to learn the classifier is defined as a surrogate
function of the following 0-1 classification error,
ˆ
L(
y
j
,y
j
)
ˆ
=
I
.
(2.5)
{
y
j
= ˆ
y
j
}
In practice, different surrogate functions of the above classification error yield
different loss functions, such as the exponential loss, the hinge loss, and the logistic
loss. All of them can be used to learn the classifier. In particular, in [
15
], the follow-
ing surrogate loss function is used, and the boosting tree algorithm is employed to
minimize the loss.
m
K
L
φ
(
y
j
,y
j
)
ˆ
=
1
−
log
P(
y
j
=
ˆ
k)I
{
y
j
=
k
}
.
(2.6)
j
=
1
k
=
Specifically, the classifier is defined with an additive model parameterized by
w
, i.e.,
F
k
(
,w)
. Given a document
x
j
,
F
k
(x
j
,w)
will indicate the degree that
x
j
belongs to category
k
. Based on
F
k
, the probability
P(
·
y
j
ˆ
=
k)
is defined with a
logistic function,
e
F
k
(x
j
,w)
s
=
1
e
F
s
(x
j
,w)
.
y
j
=
ˆ
=
P(
k)
(2.7)
In the test process, the classification results are converted into ranking scores.
In particular, the output of the classifier is converted to a probability using (
2.7
).
Suppose this probability is
P(
k)
, then the following weighted combination is
used to determine the final ranking score of a document,
y
j
=
ˆ
K
f(x
j
)
=
g(k)
·
P(
y
j
=
ˆ
k),
(2.8)
k
=
1
where
g(
·
)
is a monotone (increasing) function of the relevance degree
k
.
