ABSTRACT
Multi-Label Classification: An Overview
Grigorios Tsoumakas, Ioannis Katakis
Dept. of Informatics, Aristotle University of Thessaloniki, 54124, Greece
Nowadays, multi-label classification methods are increasingly required by modern applications, such
as protein function classification, music categorization and semantic scene classification. This paper
introduces the task of multi-label classification, organizes the sparse related literature into a structured
presentation and performs comparative experimental results of certain multi-label classification
methods. It also contributes the definition of concepts for the quantification of the multi-label nature
of a data set.
INTRODUCTION
Traditional single-label classification is concerned with learning from a set of examples that are
associated with a single label l from a set of disjoint labels L, |L| > 1. If |L| = 2, then the learning
problem is called a binary classification problem (or filtering in the case of textual and web data),
while if |L| > 2, then it is called a multi-class classification problem.
In multi-label classification, the examples are associated with a set of labels Y ⊆ L. In the past, multi-
label classification was mainly motivated by the tasks of text categorization and medical diagnosis.
Text documents usually belong to more than one conceptual class. For example, a newspaper article
concerning the reactions of the Christian church to the release of the Da Vinci Code film can be
classified into both of the categories Society\Religion and Arts\Movies. Similarly in medical diagnosis,
a patient may be suffering for example from diabetes and prostate cancer at the same time.
Nowadays, we notice that multi-label classification methods are increasingly required by modern
applications, such as protein function classification (Zhang & Zincir-Heywood, 2005), music
categorization (Li & Ogihara, 2003) and semantic scene classification (Boutell et al., 2004). In
semantic scene classification, a photograph can belong to more than one conceptual class, such as
sunsets and beaches at the same time. Similarly, in music categorization a song may belong to more
than one genre. For example, several hit songs of the popular rock band Scorpions can be
characterized as both rock and ballad.
This paper aims to serve as a starting point and reference for researchers interested in multi-label
classification. The main contributions are: a) a structured presentation of the sparse literature on
multi-label classification methods with comments on their relative strengths and weaknesses and
when possible the abstraction of specific methods to more general and thus more useful schemata, b)
the introduction of an undocumented multi-label method, c) the definition of a concept for the
quantification of the multi-label nature of a data set, d) preliminary comparative experimental results
about the performance of certain multi-label methods.
The rest of the paper is organized as follows. The next section discusses tasks that are related to multi-
label classification. Subsequently follows an organized presentation of multi-label classification
methods. The next section introduces the concept of label density and presents the metrics that have
been proposed in the past for the evaluation of multi-label classifiers. The following section presents
the comparative experiments and discusses the results, while the concluding section summarizes this
work and points to future research directions.
RELATED TASKS
A task that also belongs to the general family of supervised learning and is very relevant to multi-label
classification is that of ranking. In ranking the task is to order a set of labels L, so that the topmost
labels are more related with the new instance. There exist a number of multi-label classification
methods that learn a ranking function from multi-label data. However, a ranking of labels requires
post-processing in order to give a set of labels, which is the proper output of a multi-label classifier.
In certain classification problems the labels belong to a hierarchical structure. The dmoz open
directory for example (http://www.dmoz.org/), maintains a hierarchy of conceptual classes for the
categorization of web pages. A web page may be labelled using one or more of those classes, which
can belong to different levels of the hierarchy. The top level of the MIPS (Munich Information Centre
for Protein Sequences) hierarchy (http://mips.gsf.de/) consists of classes such as: Metabolism, Energy,
Transcription and Protein Synthesis. Each of these classes is then subdivided into more specific
classes, and these are in turn subdivided, and then again subdivided, so the hierarchy is up to 4 levels
deep (Clare & King, 2001). When the labels in a data set belong to a hierarchical structure then we
call the task hierarchical classification. If each example is labelled with more than one node of the
hierarchical structure, then the task is called hierarchical multi-label classification. In this paper we
focus on flat (non-hierarchical) multi-label classification methods.
Jin and Ghahramani (2002) call multiple-label problems, the semi-supervised classification problems
where each example is associated with more than one classes, but only one of those classes is the true
class of the example. This task is not that common in real-world applications as the one we are
studying.
Multiple-instance learning is a variation of supervised learning, where the task is to learn a concept
given positive and negative bags of instances (Maron & Lozano-Perez, 1997). Each bag may contain
many instances, but a bag is labelled positive even if only one of the instances in it falls within the
concept. A bag is labelled negative only if all the instances in it are negative.
MULTI-LABEL CLASSIFICATION METHODS
We can group the existing methods for multi-label classification into two main categories: a) problem
transformation methods, and b) algorithm adaptation methods. We call problem transformation
methods, those methods that transform the multi-label classification problem either into one or more
single-label classification or regression problems, for both of which there exists a huge bibliography
of learning algorithms. We call algorithm adaptation methods, those methods that extend specific
learning algorithms in order to handle multi-label data directly.
Problem transformation methods
To exemplify these methods we will use the data set of Table 1. It consists of four examples
(documents in this case) that belong to one or more of four classes: Sports, Religion, Science, and
Politics.
Table 1: Example of a multi-label data set
Ex. Sports Religion Science Politics
1 X X
2 X X
3 X
4 X X
There exist two straightforward problem transformation methods that force the learning problem into
traditional single-label classification (Boutell et al., 2004). The first one (dubbed PT1) subjectively or
randomly selects one of the multiple labels of each multi-label instance and discards the rest, while
the second one (dubbed PT2) simply discards every multi-label instance from the multi-label data set.
Table 2 and Table 3 show the transformed data set using methods PT1 and PT2 respectively. These
two problem transformation methods discard a lot of the information content of the original multi-
label data set and are therefore not considered further in this work.
Table 2: Transformed data set using PT1
Ex. Sports Religion Science Politics
1 X
2 X
3 X
4 X
Table 3: Transformed data set using PT2
Ex. Sports Religion Science Politics
3 X
The third problem transformation method that we will mention (dubbed PT3), considers each different
set of labels that exist in the multi-label data set as a single label. It so learns one single-label
classifier H: X → P(L) , where P(L) is the power set of L. Table 4 shows the result of transforming the
data set of Table 1 using this method. One of the negative aspects of PT3 is that it may lead to data
sets with a large number of classes and few examples per class. PT3 has been used in the past in
(Boutell et al., 2004; Diplaris et al., 2005).
Table 4: Transformed data set using PT3
Ex. Sports (Sports ∧ Politics) (Science ∧ Politics) (Science ∧ Religion)
1 X
2 X
3 X
4 X
The most common problem transformation method (dubbed PT4) learns |L| binary classifiers Hl: X →
{l, ¬l} , one for each different label l in L. It transforms the original data set into |L| data sets Dl that
contain all examples of the original data set, labelled as l if the labels of the original example
contained l and as ¬l otherwise. It is the same solution used in order to deal with a single-label multi-
class problem using a binary classifier.
For the classification of a new instance x this method outputs as a set of labels the union of the labels
that are output by the |L| classifiers:
( x)
{ l}
: H ( x)
= l
H PT 4 = U
l
l∈L
Figure 1 shows the four data sets that are constructed by PT4 when applied to the data set of Table 1.
PT4 has been used in the past in (Boutell et al., 2004; Goncalves & Quaresma, 2003; Lauser & Hotho,
2003; Li & Ogihara, 2003).
Figure 1: The four data sets that are constructed by PT4
A straightforward, yet undocumented, problem transformation method is the following (dubbed PT5):
Firstly, it decomposes each example (x, Y) into |Y| examples (x, l) for all l ∈ Y. Then it learns one
single-label coverage-based classifier from the transformed data set. Distribution classifiers are those
classifiers that can output a distribution of certainty degrees (or probabilities) for all labels in L.
Finally it post-processes this distribution to output a set of labels. One simple way to achieve this is to
output those labels for which the certainty degree is greater than a specific threshold (e.g. 0.5). A
more complex way is to output those labels for which the certainty degree is greater than a percentage
(e.g. 70%) of the highest certainty degree. Table 5 shows the result of transforming the data set of
Table 1 using this method.
Ex. Sports ¬Sports
1 X
2 X
3 X
4 X
(a)
Ex. Religion ¬Religion
1 X
2 X
3 X
4 X
(c)
Ex. Politics ¬Politics
1 X
2 X
3 X
4 X
(b)
Ex. Science ¬Science
1 X
2 X
3 X
4 X
Table 5: Transformed data set using PT5
Ex. Class
1 Sports
1 Politics
2 Science
2 Politics
3 Sports
4 Religion
4 Science
(d)
Algorithm adaptation methods
Clare and King (2001) adapted the C4.5 algorithm for multi-label data. They modified the formula of
entropy calculation as follows:
entropy
N
∑
i=
1
( S ) = − ( p(
c ) log p(
c ) + q(
c ) log q(
c ) )
i
where p(ci) = relative frequency of class ci and q(ci) = 1−p(ci). They also allowed multiple labels in
the leaves of the tree.
Adaboost.MH and Adaboost.MR (Schapire & Singer, 2000) are two extensions of AdaBoost (Freund
& Schapire, 1997) for multi-label classification. They both apply AdaBoost on weak classifiers of the
form H:X ×L → R. In AdaBoost.MH if the sign of the output of the weak classifiers is positive for a
new example x and a label l then we consider that this example can be labelled with l, while if it's
negative then this example is not labelled with l. In AdaBoost.MR the output of the weak classifiers is
considered for ranking each of the labels in L.
Although these two algorithms are adaptations of a specific learning approach, we notice that at their
core, they actually use a problem transformation (dubbed PT6): Each example (x, Y) is decomposed
into |L| examples (x, l, Y[l]), for all l ∈ L, where Y[l] = 1 if l ∈ Y, and [l] = −1 otherwise. Table 6
shows the result of transforming the data set of Table 1 using this method.
ML-kNN (Zhang & Zhou, 2005) is an adaptation of the kNN lazy learning algorithm for multi-label
data. Actually this method follows the paradigm of PT4. In essence, ML-kNN uses the kNN algorithm
independently for each label l: It finds the k nearest examples to the test instance and considers those
that are labelled at least with l as positive and the rest as negative. What mainly differentiates this
method from the application of the original kNN algorithm to the transformed problem using PT4 is
the use of prior probabilities. ML-kNN has also the capability of producing a ranking of the labels as
an output.
i
i
i
Table 6: Transformed data set using PT6
Ex. l Y[l]
1 Sports 1
1 Religion -1
1 Science -1
1 Politics 1
2 Sports -1
2 Religion -1
2 Science 1
2 Politics 1
3 Sports 1
3 Religion -1
3 Science -1
3 Politics -1
4 Sports -1
4 Religion 1
4 Science 1
4 Politics -1
Luo and Zincir-Heywood (2005) present two systems for multi-label document classification, which
are also based on the kNN classifier. The main contribution of their work is on the pre-processing
stage for the effective representation of documents. For the classification of a new instance, the
systems initially find the k nearest examples. Then for every appearance of each label in each of these
examples, they increase a corresponding counter for that label. Finally they output the N labels with
the largest counts. N is chosen based on the number of labels of the instance. This is an inappropriate
strategy for real-world use, where the number of labels of a new instance is unknown.
McCallum (1999) defines a probabilistic generative model according to which, each label generates
different words. Based on this model a multi-label document is produced by a mixture of the word
distributions of its labels. The parameters of the model are learned by maximum a posteriori
estimation from labelled training documents, using Expectation Maximization to calculate which
labels were both the mixture weights and the word distributions for each label. Given a new document
the label set that is most likely is selected with Bayes rule. This approach for the classification of a
new document actually follows the paradigm of PT3, where each different set of labels is considered
independently as a new class.
Elisseeff and Weston (2002) present a ranking algorithm for multi-label classification. Their
algorithm follows the philosophy of SVMs: it is a linear model that tries to minimize a cost function
while maintaining a large margin. The cost function they use is ranking loss, which is defined as the
average fraction of pairs of labels that are ordered incorrectly. However, as stated earlier, the
disadvantage of a ranking algorithm is that it does not output a set of labels.
Godbole and Sarawagi (2004) present two improvements for the Support Vector Machine (SVM)
classifier in conjunction with the PT4 method for multi-label classification. The first improvement
could easily be abstracted in order to be used with any classification algorithm and could thus be
considered an extension to PT4. The main idea is to extend the original data set with |L| extra features
containing the predictions of each binary classifier. Then a second round of training |L| new binary
classifiers takes place, this time using the extended data sets. For the classification of a new example,
the binary classifiers of the first round are initially used and their output is appended to the features of
the example to form a meta-example. This meta-example is then classified by the binary classifiers of
the second round. Through this extension the approach takes into consideration the potential
dependencies among the different labels. Note here that this improvement is actually a specialized
case of applying Stacking (Wolpert, 1992) (a method for the combination of multiple classifiers) on
top of PT4.
The second improvement of (Godbole & Sarawagi, 2004) is SVM-specific and concerns the margin of
SVMs in multi-label classification problems. They improve the margin by a) removing very similar
negative training instances which are within a threshold distance from the learnt hyperplane, and b)
removing negative training instances of a complete class if it is very similar to the positive class,
based on a confusion matrix that is estimated using any fast and moderately accurate classifier on a
held out validation set. Note here that the second approach for margin improvement is actually SVM
independent. Therefore, it could also be used as an extension to PT4.
MMAC (Thabtah, Cowling & Peng, 2004) is an algorithm that follows the paradigm of associative
classification, which deals with the construction of classification rule sets using association rule
mining. MMAC learns an initial set of classification rules through association rule mining, removes
the examples associated with this rule set and recursively learns a new rule set from the remaining
examples until no further frequent items are left. These multiple rule sets might contain rules with
similar preconditions but different labels on the right hand side. Such rules are merged into a single
multi-label rule. The labels are ranked according to the support of the corresponding individual rules.
ISSUES
How much multi-label is a data set?
Not all data sets are equally multi-label. In some applications the number of labels of each example is
small compared to |L|, while in others it is large. This could be a parameter that influences the
performance of the different multi-label methods. We here introduce the concepts of label cardinality
and label density of a data set. Let D be a multi-label data set consisting of |D| multi-label examples
(xi, Yi), i = 1..|D|.
Definition 1: Label cardinality of D is the average number of labels of the examples in D:
D
1
LC(D)= ∑
i=
D 1
Definition 2: Label density of D is the average number of labels of the examples in D divided by |L|:
D
1
LD(D) = ∑
=
D i 1
Yi
Yi
L
Label cardinality is independent of the number of labels |L| in the classification problem, and is used
to quantify the number of alternative labels that characterize the examples of a multi-label training
data set. Label density takes into consideration the number of labels in the classification problem.
Two data sets with the same label cardinality but with a great difference in the number of labels
(different label density) might not exhibit the same properties and cause different behaviour to the
multi-label classification methods. The two metrics are related to each other: LC(D) = |L| LD(D).
Evaluation metrics
Multi-label classification requires different metrics than those used in traditional single-label
classification. This section presents the various metrics that have been proposed in the literature. Let
D be a multi-label evaluation data set, consisting of |D| multi-label examples (xi, Yi), i = 1..|D|, Yi ⊆ L.
Let H be a multi-label classifier and Zi = H(xi) be the set of labels predicted by H for example xi.
Schapire and Singer (2000) consider the Hamming Loss, which is defined as:
1
HammingLoss(H, D) = ∑
=
D
D i 1
YiΔZ
L
Where Δ stands for the symmetric difference of two sets and corresponds to the XOR operation in
Boolean logic.
The following metrics are used in (Godbole & Sarawagi, 2004) for the evaluation of H on D:
1
Accuracy(H, D) = ∑
=
1
Precision(H, D) = ∑
=
1
Recall(H, D) = ∑
=
Y I Z
D
i
i
D i 1 Yi
U Z i
Y I Z
D
i
D i 1 Z i
Y I
Z
D
i
D i 1 Yi
i
i
i
Boutell et al. (2004) give a more generalized version of the above accuracy using a parameter α ≥ 0,
called forgiveness rate:
D
1 ⎛ Yi
I Z
Accuracy(H, D) = ∑ ⎜
D ⎜
= 1 ⎝ Yi
U Z
i i
This parameter is used in order to control the forgiveness of errors that are made in predicting labels.
They also give an even more generalized version of the accuracy by introducing two additional
parameters in order to allow different costs for false positives and true negatives. These two general
measures of accuracy are too complex, due to the additional parameters, but could be useful in certain
applications.
EXPERIMENTAL COMPARISON OF PT METHODS
We implemented the PT3, PT4 and PT6 methods in Java, within the framework of the WEKA (Witten
& Frank, 1998) library of machine learning algorithms, and made the software publicly available at
the following URL (mlkd.csd.auth.gr/multilabel.html). We experimented with the three PT methods
in conjunction with the following classifier learning algorithms: kNN (Aha, Kibler & Albert), C4.5
(Quinlan, 1993), Naive Bayes (John & Langley, 1995) and SMO (Platt, 1998). For performance
evaluation, we used the HammingLoss, Accuracy, Precision and Recall metrics that were presented in
the previous section.
We experimented on the following multi-label data sets: genbase (Diplaris et al., 2005) and yeast
(Elisseeff & Weston, 2002) are biological data sets that are concerned with protein function
classification and gene function classification respectively. The scene data set (Boutell et al., 2004)
contains data related to a scene classification problem. These data sets were retrieved from the site of
the Support Vector Classification library LIBSVM (Chang & Lin, 2001), and transformed to a
specific format that is suitable for our software, based on the ARFF file format of the WEKA library.
The transformed data sets are also available at the aforementioned URL.
i
⎞
⎟
⎠
α
The details of the data sets, such as the number of examples, the number of numeric and discrete
attributes the number of classes and their label density are given in Table 7. We notice that genbase
(LD=0.05) and scene (LD=0.18) are quite sparse multi-label data sets with less than 1.5 labels per
example on average. The yeast dataset on the other hand is denser (LD=0.30) with more than 4 labels
per example on average.
Table 7: Examples, numeric and discrete attributes, labels and LD of datasets
Examples Attributes
Data set Train Test Numeric Discrete Labels
Label
Density
Label
Cardinality
genbase 463 199 0 1185 27 0.05 1.35
yeast 1500 917 103 0 14 0.30 4.25
scene 1211 1196 294 0 6 0.18 1.08
Table 8 presents analytical results on the three data sets. We will first discuss the results in terms of
accuracy. The combination of the PT3 method together with the SMO learning algorithm gives the
best results in each of the three data sets. In addition the PT3 method has the highest mean accuracy
for all learning algorithms in each of the three data sets, followed by PT4 and then by PT6. This
means that it is the best method independently of learning algorithm in each of the three data sets.
This is an interesting result, given that the PT3 method is not so popular in the literature compared to
PT4.
We will now discuss the results in terms of Hamming loss. In genbase the best results are obtained
with PT4 in combination with either kNN or SMO. In yeast the best results are obtained again with
PT4 in combination with SMO, while in scene the best results are obtained with PT3 in conjunction
with SMO. Independently of the algorithm used, PT3 is the best method in scene, PT4 in genbase and
PT6 in yeast.
One noteworthy result is that PT6 does not perform well in combination with SMO for the scene and
genbase data sets. Note that these two data sets are quite sparse as LD(scene)=0.18 and
LD(genbase)=0.05. This means that after the transformation, the class attribute will have a large
number of examples with a value of -1. It seems that in these cases SMO learns to predict always -1.
This leads to zero accuracy, precision and recall, while Hamming loss becomes equal to the label
density of the data set.
Table 8: Resuls on the three data sets
genbase
PT3 PT4 PT6
Metric kNN C4.5 NB SMO kNN C4.5 NB SMO kNN C4.5 NB SMO
HamLoss 0,004 0,046 0,057 0,001 0,000 0,001 0,035 0,000 0,025 0,002 0,103 0,046
Accuracy 0,964 0,984 0,340 0,993 0,989 0,987 0,273 0,991 0,543 0,984 0,019 0,000
Recall 0,990 0,995 0,347 1,000 0,997 0,995 0,276 0,997 0,548 0,994 0,020 0,000
Precision 0,964 0,984 0,340 0,993 0,992 0,992 0,273 0,993 0,543 0,990 0,117 0,000
yeast
PT3 PT4 PT6
Metric kNN C4.5 NB SMO kNN C4.5 NB SMO kNN C4.5 NB SMO
HamLoss 0,229 0,286 0,243 0,206 0,243 0,259 0,301 0,200 0,208 0,259 0,261 0,233
Accuracy 0,495 0,399 0,464 0,530 0,479 0,423 0,421 0,502 0,514 0,423 0,329 0,337
Recall 0,628 0,528 0,608 0,672 0,601 0,593 0,531 0,711 0,665 0,593 0,604 0,748
Precision 0,596 0,529 0,575 0,615 0,596 0,561 0,610 0,579 0,623 0,561 0,407 0,337
scene
PT3 PT4 PT6
Metric kNN C4.5 NB SMO kNN C4.5 NB SMO kNN C4.5 NB SMO
HamLoss 0,113 0,148 0,139 0,100 0,125 0,139 0,247 0,114 0,147 0,139 0,357 0,181
Accuracy 0,668 0,572 0,603 0,704 0,637 0,513 0,435 0,571 0,242 0,513 0,076 0,000
Recall 0,703 0,598 0,631 0,737 0,669 0,534 0,443 0,596 0,253 0,534 0,078 0,000
Precision 0,668 0,584 0,633 0,713 0,651 0,611 0,816 0,628 0,243 0,611 0,317 0,000
CONCLUSIONS AND FUTURE WORK
This work was involved with the task of multi-label classification: It introduced the problem, gave an
organized presentation of the methods that exist in the literature and provided comparative
experimental results for some of these methods. To the best of our knowledge, there is no other
review paper on the interesting and upcoming task of multi-label classification.
In the future we intend to perform a finer-grained categorization of the different multi-label
classification methods and perform more extensive experiments with more data sets and methods. We
also intend to perform a comparative experimental study of problem adaptation methods.
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