Information Technology Reference
InDepth Information
MAP
IA
@
k
=
P(c

q)
MAP@
k.
(6.16)
c
Experimental results showed that the proposed method can significantly outper
form previous methods in terms of the intentaware measures.
In [
4
], it is formally pointed out that in most cases the diversification problem
can be characterized as a bicriteria optimization problem. That is, diversification
can be viewed as combining both ranking (presenting more relevant results in the
higher positions) and clustering (grouping documents satisfying similar intents) and
therefore addresses a loosely defined goal of picking a set of the most relevant but
novel documents. A very general objective function considering the above aspects
can be formulated as follows.
L
S
k
,q,f(
)
,
·
), d(
·
,
·
(6.17)
where
S
k
is the subset of documents presented at the top
k
positions,
q
is the given
query,
f(
)
is a distance function.
Then a set of simple properties (called axioms) that any diversification system
ought to satisfy are proposed as follows.
3
·
)
is a relevance function, and
d(
·
,
·
•
Scale invariance:
Informally, this property states that the set selection function
should be insensitive to the scaling of the input functions
f(
·
)
and
d(
·
,
·
)
.
•
Consistency:
Consistency states that making the output documents more relevant
and more diverse, and making other documents less relevant and less diverse
should not change the output of the ranking.
•
Richness:
Informally speaking, the richness condition states that we should be
able to achieve any possible set as the output, given the right choice of relevance
and distance functions.
•
Stability:
The stability condition seeks to ensure that the output set does not
change arbitrarily with the output size. That is, the best top(
k
+
1) subset should
be a super set of the best top
k
subset.
•
Independence of irrelevant attributes:
This axiom states that the score of a set is
not affected by most attributes of documents outside the set.
•
Monotonicity:
Monotonicity simply states that the addition of any document does
not decrease the score of the set.
•
Strength of relevance:
This property ensures that no function
L
ignores the rele
vance function.
•
Strength of similarity:
This property ensures that no function
L
ignores the dis
tance function.
It is pointed out in [
4
], however, that no function
L
can satisfy all the eight ax
ioms. For example, the objective function in [
1
] violates the axioms of stability and
3
Please note that these axioms might not be as necessary as claimed in some cases. For example, it
is sometimes reasonable that a good diversification system does not possess the stability property,
since the stability property somehow implies greedy systems which might not be optimal.