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Fig. 3.8
Training multiple
rankers
the model trained from categories
k
and
l
is denoted by
f
k,l
, then the final ranking
results can be attained by using the weighted BordaCount aggregation.
4
f(x)
=
α
k,l
f
k,l
(x).
(3.20)
k,l
Here the combination coefficient
α
k,l
can be pre-specified or learned from a sep-
arate validation set. The experimental results in [
26
] show that by considering more
information about the judgment, the ranking performance can be significantly im-
proved over Ranking SVM. Note that the technology used in MHR actually can be
extended to any other pairwise ranking algorithms.
3.3.2 Magnitude-Preserving Ranking
In [
14
], Cortes et al. also attempt to tackle the first problem with the pairwise
approach. In particular, they propose keeping the magnitude of the labeled pref-
erences, and accordingly use the so-called
magnitude-preserving loss
(MP loss),
hinge magnitude-preserving loss
(HMP loss), and SVM regression loss (SVR loss)
for learning to rank. These three loss functions can effectively penalize a pairwise
misranking by the magnitude of predicted preference or the
β
th power of that mag-
nitude. That is, considering the property of the power function
x
β
, if the loss on a
pair is large, it will be highly penalized if
β
is set to be large.
4
Note that there are many algorithms for rank aggregation proposed in the literature, such as Bor-
daCount [
2
,
5
,
16
], median rank aggregation [
17
], genetic algorithm [
4
], fuzzy logic-based rank
aggregation [
1
], and Markov chain-based rank aggregation [
16
]. Although BordaCount is used
in [
26
] as an example, it by no means dictates that other methods cannot be used for the same
purpose.