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independence of irrelevant attributes. Therefore, one can only hope for diversifica-
tion functions that satisfy a subset of the axioms. A few such examples are given as
follows:
1. Max-sum diversification, which satisfies all the axioms, except stability.
2
λ
u,v
∈
S
1
)
u
∈
S
L(S)
=
(k
−
f(u)
+
d(u,v).
(6.18)
2. Max-min diversification, which satisfies all the axioms except consistency and
stability.
L(S)
=
min
u
∈
S
f(u)
+
λ
min
u,v
∈
S
d(u,v).
(6.19)
3. Mono-objective formulation, which satisfies all the axioms except consistency.
1
v
∈
U
λ
L(S)
=
f(u)
+
d(u,v).
(6.20)
|
U
|−
u
∈
S
In addition to the two pieces of work introduced above, there are also many other
works on learning diverse ranking. Actually, the task of learning diverse ranking
has become a hot research topic in the research community. In 2009, the TREC
conference even designed a special task for search result diversification. The goal of
the diversity task is to return a ranked list of pages that together provide complete
coverage for a query, while avoiding excessive redundancy in the result list.
In the task, 50 queries are used. Subtopics for each query are based on infor-
mation extracted from the logs of a commercial search engine, and are roughly
balanced in terms of popularity. Each topic is structured as a representative set of
subtopics, each related to a different user need. Documents are judged with respect
to the subtopics. For each subtopic, the human assessors will make a binary judg-
ment as to whether or not the document satisfies the information need associated
with the subtopic.
α
-NDCG [
2
] and MAP
IA
[
1
] are used as the evaluation measures.
For more information, one can refer to the website of the task:
http://plg.uwaterloo.
ca/~trecweb/
.
6.3 Discussions
In this chapter, we have introduced some existing works on relational ranking. While
these works have opened a window to this novel task beyond conventional learning
to rank, there are still many issues that need to be further investigated.
•
As mentioned before, it is not clear how the general relational ranking framework
can be used to solve the problem of learning diverse ranking. It would be interest-
ing to look into this issue, so as to make the general relational ranking framework
really general.