Information Technology Reference
In-Depth Information
scores.
max
i
w
i
ξ
i
,
min
i
e
i,j
ξ
i
ξ
j
,
(13.17)
j
=
i
s.t.
ξ
i
∈{
0
,
1
}
and
ξ
i
=
t,
i
where
t
denotes the number of selected features,
ξ
i
indicates that the
i
th feature is
selected,
w
i
denotes the importance score of the
i
th feature, and
e
i,j
denotes the
similarity between the
i
th and
j
th features.
Since the above multi-objective optimization problem is not easy to solve, it is
converted to a single-objective optimization problem by linearly combining the orig-
inal two objectives. Then, a greedy search method is used to optimize the new prob-
lem as follows.
•
Construct an undirected graph
G
, in which each node represents a feature, the
weight of the
i
th node is
w
i
and the weight of an edge between the
i
th and
j
th
nodes is
e
i,j
.
•
Follow the below steps in an iterative manner.
- Select the node with the largest weight. Without loss of generality, suppose that
the selected node is
k
i
.
- A punishment is conducted on all the other nodes according to their similarities
with the selected node. That is
w
j
←
2
c
, where
c
is a constant.
- Remove node
k
i
from graph
G
together with all the edges connected to it, and
put it into the selected feature set.
w
j
−
e
k
i
,j
·
•
Output the selected features.
According to the experiments in [
17
], the above method is both effective and
efficient in selecting features for learning to rank.
13.4 Summary
In this chapter, we have discussed the data issue in learning to rank. Data is the root
of an algorithm. Only if we have informative and reliable data can we get effective
ranking models. The studies on the data issue are still limited. More research on this
topic will greatly advance the state of the art of learning to rank.
13.5 Exercises
13.1 Compare different user click models introduced in this chapter, and discuss
their pros and cons.
