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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
1. Max-sum diversification, which satisfies all the axioms, except stability.
2 λ
u,v S
1 )
u S
2. Max-min diversification, which satisfies all the axioms except consistency and
u S
λ min
u,v S
3. Mono-objective formulation, which satisfies all the axioms except consistency.
v 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.
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