˖ڍመڙጲ
http://www.paper.edu.cn
mance in comparison with its counterparts designed specifically for MLC.
The rest of the paper is structured as follows: We firstly introduce the required background
in the field of multi-dimensional classification in Section 2. Then we introduce MLKT in Section
3. Next, we present the details of the distance metric learning method in Section 4. We then
experimentally evaluate the proposed schemes in Section 5. Finally, we give concluding remarks
in Section 6.
1 Background
In this section, we review basic multi-dimensional classifiers.
In MDC, we have N labeled instances D = {(x
i
, y
i
)}
N
i=1
from which we wish to build
a classifier that associates multiple class values with each data instance. The data instance
is represented by a vector of d values x = (x
1
, . . . , x
d
), each drawn from some input domain
X
1
× · · · × X
d
. And the classes are represented by a vector of m values y = (y
1
, . . . y
m
) from
the domain Y
1
× · · · × Y
m
where each Y
j
= {1, . . . , K
j
} is the set of possible values for the
jth class variable. Specifically, we seek to build a classifier f that assigns each instance x to a
vector y of class values:
f : X
1
× · · · × X
d
→ Y
1
× · · · × Y
m
x : (x
1
, . . . , x
d
) 7→ y : (y
1
, . . . y
m
)
Independent classifiers method (IC) is a straightforward method for MDC. It trains m
classifiers f := (f
1
, . . . , f
m
) for each class variable. Specifically, a standard multi-class classifier
f
j
learns to associate one of the values y
j
∈ Y
j
to each data instance, where f
j
: X
1
×· · ·×X
d
→
Y
j
. However, it is unable to capture the dependencies among classes and suffers low accuracies
as illustrated in [5, 26, 27].
MDC has attracted more attentions recently and many multi-dimensional classifiers for
modeling the output structure of MDC have been proposed in recent years. As presented in
the introduction section, there are two main strategies:
1. Explicit representation of the dependence structure between class variables.
Classifier chains model (CC)[5, 6, 7, 28], Classifier trellises (CT) [26] and Multi-dimensional
Bayesian network classifiers (MBCs) [8, 9] were recently proposed methods following this
strategy for MDC. Specifically,
classifier chains model (CC) learns m classifiers, one for each class variable. These clas-
sifiers are linked at random order, such that the jth classifier uses as input features not
only the instance, but also the output predictions of the previous j − 1 classifiers, namely
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