Balanced Sampling Method for Imbalanced Big Data Using AdaBoost
Hong Gu and Tao Song
School of Control Science and Engineering, Dalian University of Technology, Dalian, China
Keywords:
Big data, Class Imbalance Learning, Sampling, Boosting, Bagging, Parallel Algorithms.
Abstract:
With the arrival of the era of big data, processing large volumes of data at much faster rates has become
more urgent and attracted more and more attentions. Furthermore, many real-world data applications present
severe class distribution skews and the underrepresented classes are usually of concern to researchers. Variants
of boosting algorithm have been developed to cope with the class imbalance problem. However, due to the
inherent sequential nature of boosting, these methods can not be directly applied to efficiently handle large-
scale data. In this paper, we propose a new parallelized version of boosting, AdaBoost.Balance, to deal with
the imbalanced big data. It adopts a new balanced sampling method which combines undersampling methods
with oversampling methods and can be simultaneously calculated by multiple computing nodes to construct
a final ensemble classifier. Consequently, it is easily implemented by the parallel processing platform of big
data such as the MapReduce framework.
1 INTRODUCTION
Big data is a dynamic definition whose large quan-
tity and complexity makes it difficult to capture,
store, manage, search, share, transfer, mine, ana-
lyze and visualize using existing data management
tools, data processing applications and data mining
approaches (Manyika et al., 2011). It is generated
in many scientific and real-world areas such as ge-
nomics, proteomics, bioinformatics (Greene et al.,
2014), telecommunications, health care, pharmaceu-
tical or financial businesses. Big data is character-
ized with volume, velocity, variety, veracity, validity,
volatility, variability or value (Laney, 2001; del R
´
ıo
et al., 2014). Consequently, it is vital to develop more
suitable and faster algorithms to efficiently deal with
such massive amounts of data.
What makes this challenge even more difficult is
that most of these big data also exhibit imbalanced
class distributions, in other words, the number of data
that represent one class is much lower than the ones
of the other classes. Moreover, the minority class
is usually the main interest and more important, i.e.,
there is always an implicit assumption in class imbal-
ance learning that the minority class has higher cost
than the majority class. Imbalanced learning prob-
lem has become an important issue in the field of
machine learning and a large amount of techniques
have been developed trying to address this problem
(Chawla et al., 2004; He and Garcia, 2009). De-
pending on how they deal with class imbalance, these
methods can be categorized into three groups: al-
gorithm level approaches, data level techniques and
cost-sensitive methods (del R
´
ıo et al., 2014; Galar
et al., 2012). The algorithm level approaches create
all new algorithms or modify current existing meth-
ods to pay more attention to positive samples (mi-
nority class) than negative samples (majority class).
Data level techniques consist of a preprocessing step
to modify an imbalanced data set in order to pro-
vide a balanced distribution, usually by oversampling
methods, undersampling methods and hybrid meth-
ods (combine oversampling with undersampling) (Es-
tabrooks et al., 2004). Cost-sensitive methods com-
bine the ideas from both data and algorithm level ap-
proaches by using different cost matrices to consider
costs of misclassifications, and its usual practice is
to adopt higher misclassification costs for instances
of the minority class and minimize the overall cost
(Zadrozny et al., 2003; Sun et al., 2007).
In addition to these methods, a large number of
techniques based on ensemble learning have been
developed to solve the problem of class imbalance
(Galar et al., 2012). Ensemble methods train multiple
weak learners and then combine them to construct a
strong learner by combination methods such as aver-
aging, voting and learning, etc., and it is well known
that an ensemble is usually significantly more accu-
189
Gu H. and Song T..
Balanced Sampling Method for Imbalanced Big Data Using AdaBoost.
DOI: 10.5220/0005254601890194
In Proceedings of the International Conference on Bioinformatics Models, Methods and Algorithms (BIOINFORMATICS-2015), pages 189-194
ISBN: 978-989-758-070-3
Copyright
c
2015 SCITEPRESS (Science and Technology Publications, Lda.)
rate than a single learner. Ensemble diversity (the
difference among the individual learners) is neces-
sary and plays an important role in ensemble learning,
since there would be no performance improvement if
identical individual learners were combined. Boost-
ing (Schapire, 1990; Freund and Schapire, 1995) and
Bagging (Breiman, 1996) are the most representative
among the ensemble learning algorithms and have al-
ready achieved great success in many real-world ap-
plications. The series of boosting algorithms began
to develop from the proof of weak learnable theo-
rem (Schapire, 1990), i.e., the equivalence conjecture
of strong and weak learnability (Kearns and Valiant,
1994). Bagging contains two key elements: boot-
strap and aggregation. It adopts bootstrap sampling
(Efron and Tibshirani, 1994) to generate the data sub-
sets for training different base learners and applies
voting or averaging for aggregating the outputs of the
base learners.
In general, the members of boosting family are se-
quential ensemble methods where the base learners
are generated sequentially. The basic motivation of
sequential methods is to exploit the dependence be-
tween the base learners, where the later learners fo-
cus more on the mistakes made by the former. While
the base learners of parallel ensemble methods repre-
sented by bagging are generated in parallel. The basic
motivation of parallel ensemble methods is to exploit
the independence between the base learners, since the
error can be reduced dramatically by combining in-
dependent base learners (Zhou, 2012). The paral-
lel architecture of bagging make it easier to achieve
fast, scalable and parallel implementations by using
MapReduce (Dean and Ghemawat, 2008) framework.
MapReduce is a programming model and an asso-
ciated implementation for processing and generating
large data sets. It abstracts the calculation process in
two phases: Map divides the original set into indepen-
dent subsets and distributes them to worker nodes; Re-
duce combines the partial solutions in a way to form
the final output. However, there still are class imbal-
ance problems when directly using the MapReduce to
process the imbalanced big data (because the subsets
obtained in the Map phase still present severe class
distribution skews).
In this work, we present an new technique which
combines both bagging and boosting to deal with two-
class imbalanced big data, where there is a positive
(minority) class,with the lowest number of instances,
and a negative (majority) class, with the highest num-
ber of instances. Specifically, a balanced resampling
method is applied in the data preprocessing phase. It
combines random oversampling with random under-
sampling or SMOTE (Chawla et al., 2011) to divide
the original imbalanced set into independent balanced
subsets, as well as takes the relationship between the
imbalance ratio (IR, the size of majority class divided
by that of minority class) and the computing resource
(number of computing nodes) into account. The pur-
pose of considering this relationship is to fully exploit
useful information of the majority class and increase
the ensemble diversity by SMOTE under some com-
puting resource. Then, boosting is running on these
independent balanced subsets in parallel simultane-
ously. Finally, a single ensemble is obtained which
is an ensemble of ensembles. To be brief, we use bag-
ging as the main ensemble learning method and train
each bag using boosting. Consequently, our method
combines the advantages of both boosting and bag-
ging, that boosting mainly reduces bias while bagging
mainly reduces variance (Maclin and Opitz, 2011).
The experimental results indicate that our method can
effectively deal with the class imbalance problem. In
addition, due to the parallel nature of our method, it is
easier to be implemented on the MapReduce platform.
2 MATERIALS AND METHODS
Our method is described below in the following
aspects: the AdaBoost algorithm, the Balance-
Sampling algorithm, the AdaBoost.Balance algo-
rithm (includes AdaBoost.BSR and AdaBoost.BSS),
database and performance evaluation criteria.
2.1 AdaBoost
The AdaBoost (Freund and Schapire, 1995) algorithm
is a representative of boosting family which resolves
many practical issues of the early boosting algorithm.
The input of AdaBoost is a training set of n labeled
samples D
n
=
{
(x
1
,y
1
),...,(x
n
,y
n
)
}
, where x
i
∈ X (X
represents the instance space), y
i
∈ Y (Y =
{
−1,+1
}
is the set of labels). AdaBoost repeatedly calls the
given weak learner (base classifier), whose main idea
is to maintain a weight distribution on the training
set. The weak learners have to be slightly better than
a random guess. The weight of sample (x
1
,y
1
) is
denoted as p
t
i
in the tth iteration (t = 1,. . . , T , T is
the number of iterations). Initially, the weights of
all the examples are set to be equal (1/n). But the
weights of the misclassified instances will increase in
each iteration, in order to force weak learner to fo-
cus on the difficulties in training set. The task of the
weak learner is to find a suitable weak hypothesis: h
t
:
X → [0, 1] based on the distribution
~
P
t
. When coping
with the two-class classification problem, the range of
h
t
are two values:
{
−1,+1
}
. Therefore, the learner’s
BIOINFORMATICS2015-InternationalConferenceonBioinformaticsModels,MethodsandAlgorithms
190
task is to minimize the error ε
t
= Pr
i∼
~
P
t
[h
t
(x
i
) 6= y
i
].
Once the h
t
is obtained, AdaBoost selects a parameter
α
t
⊆ R, this parameter intuitively measure the correct-
ness or the degree of importance of h
t
, i.e., a learner
with lower error rate gets higher weight. The final
hypothesis H is obtained by combining T weak hy-
pothesis together using weighted majority vote after
T cycles. Typically, AdaBoost sets α
t
=
1
2
log
1−ε
t
ε
t
for the two-class classification problem. In general,
AdaBoost is an ensemble learning method which iter-
atively induces a strong classifier from a pool of weak
hypotheses.
Algorithm 1: AdaBoost.
Input: Training set of n labeled samples
D
n
=
{
(x
1
,y
1
),...,(x
n
,y
n
)
}
Number of iterations T
Weak learning algorithm WeakLearn
Output: The final classifier H
1: Initialize w
1
i
=
1
n
, i = 1,...,n
2: for t = 1,...,T do
3: Set the distribution
~
P
t
=
~w
t
∑
n
i=1
w
t
i
4: Call WeakLearn, providing it with distribu-
tion
~
P
t
, get back a hypothesis h
t
: X → [0, 1]
5: Calculate the error of h
t
:
ε
t
=
∑
n
i=1
p
t
i
|
h
t
(x
i
) − y
i
|
6: Set β
t
= (1 − ε
t
)
ε
t
7: Set the weight of h
t
: α
t
=
1
2
log(β
t
)
8: Set the new weights vector to be
w
t+1
i
= w
t
i
β
1−
|
h
t
(x
i
)−y
i
|
t
9: end for
10: Set the ensemble’s threshold: θ =
1
2
∑
T
t=1
α
t
11: Return H (x) = sgn
∑
T
t=1
α
t
h
t
(x) − θ
2.2 The Balance-sampling Algorithm
The purpose of using sampling methods in class im-
balance problems is to modify an imbalanced data set
by some mechanisms to provide a balanced distribu-
tion for training a classifier. Among the sampling
methods, random undersampling methods randomly
remove the majority class examples or randomly se-
lect a subset of examples from the original majority
class set to make the size of this subset the same as
the minority class. Random oversampling methods
randomly select examples from the original minor-
ity class set and augment original set by replicating
the selected examples and adding them to it until the
size is equal to that of majority class set. However,
randomly removing the majority class examples may
lose some useful information, while randomly dupli-
cating the minority class examples may increase the
risk of overfitting. To relax those problems, many
advanced resampling methods have been developed.
For example, the one-sided sampling method (Kubat
et al., 1997) selectively remove the majority class ex-
amples in order to keep more informative examples,
SMOTE generates synthetic examples by randomly
interpolating between a minority class example and
one of its neighbors from the same class instead of
exact copies to reduce the risk of overfitting. In addi-
tion, it has been empirically evaluated that neither the
oversampling nor the undersampling alone is always
the best one to use, and a combining strategy could be
useful and effective (Estabrooks et al., 2004). Conse-
quently, we introduce a way to combine the two re-
sampling methods.
The proposed Balance-Sampling algorithm com-
bines random oversampling with random undersam-
pling or SMOTE to divides the original imbalanced
set into independent balanced subsets. It determines
the size of majority class examples for each subset
by the ratio of imbalance ratio R and the number of
computing workers M. When
R
M
≥ 1, the size of ma-
jority class examples for each computing worker is
selected as
|
N
k
|
=
|
N
|
M
, and the size of minority class
example subset is determined as
|
P
k
|
=
|
N
k
|
. In other
cases of
R
M
, the size of majority class example sub-
set is selected as
|
N
k
|
=
|
N
|
R
, and the size of minority
class example subset is the same as that of the original
minority class example set. In all cases, union of all
the majority class example subsets is able to contains
as many majority class examples as possible, i.e., the
Balance-Sampling algorithm can fully exploit useful
information of the majority class.
In line 5 and 11, we used random under-sampling
method to randomly select majority class examples
from the original dataset N for N
k
until the number
|
N
k
|
is achieved. In line 6, according to different
under-sampling methods, the Balance-Sampling al-
gorithm can be classified as BSR (Balance-Sampling
by Random under-sampling) and BSS (Balance-
Sampling by the SMOTE algorithm).
2.3 The AdaBoost.Balance Algorithm
The AdaBoost.Balance algorithm is proposed based
on the AdaBoost algorithm and the Balance-Sampling
algorithm. It is an ensemble of ensembles, i.e.,
the Balance-Sampling algorithm is firstly taken as
the bootstrap sampling, then AdaBoost is applied
to train a base learner on each obtained balanced
subset and finally the weighted majority voting is
adopted for aggregating the outputs of the base learn-
ers. Consequently, our method combines the advan-
tages of both boosting and bagging, that boosting
BalancedSamplingMethodforImbalancedBigDataUsingAdaBoost
191
mainly reduces bias while bagging mainly reduces
variance. Moreover, because AdaBoost.Balance takes
bagging as the main ensemble learning method, it has
the same parallel nature as bagging and that makes
AdaBoost.Balance easier to be implemented on the
MapReduce platform.
In line 1, when using the BSR method the
AdaBoost.Balance algorithm is denoted as Ad-
aBoost.BSR and it is represented as AdaBoost.BSS
when adopting the BSS method.
Algorithm 2: The Balance-Sampling algorithm.
Input: The training sets D =
{
P,N
}
P is a set of minority class examples
N is a set of majority class examples
Number of computing workers M
Output: Balanced training sets
D
1
n
1
,...,D
M
n
M
1: Calculate the Imbalance Ratio (IR): R =
|
N
|
|
P
|
2: if
R
M
≥ 1 then
3: for k = 1,. . . , M do
4:
|
N
k
|
=
|
N
|
M
,
|
P
k
|
=
|
N
k
|
5: Undersampling N
k
from N
6: Oversampling P
k
from P
7: end for
8: else
9: for k = 1,. . . , M do
10:
|
N
k
|
=
|
N
|
R
,
|
P
k
|
=
|
P
|
11: Undersampling N
k
from N
12: P
k
= P
13: end for
14: end if
15: Return
D
1
n
1
,...,D
M
n
M
, where
D
k
n
k
=
{
P
k
,N
k
}
, n
k
=
|
P
k
|
+
|
N
k
|
Algorithm 3: The AdaBoost.Balance.
Input: Training set D =
{
P,N
}
Number of boosting iterations T
Number of computing workers M
Weak learning algorithm WeakLearn
Output: The final classifier H
1:
D
1
n
1
,...,D
M
n
M
←Balance-Sampling(D)
2: for k = 1,...,M do
3: H
k
(x) ←AdaBoost
D
k
N
k
,T
4: end for
5: Return
H (x) = sgn
∑
M
k=1
∑
T
t=1
α
k
t
h
k
t
(x) −
∑
M
k=1
θ
k
3 EXPERIMENTS
In this section, we demonstrate the performance of
our proposed algorithms in term of AUC (Area Under
the receiver operating characteristic Curve) (Bradley,
1997). Eleven UCI data sets (Blake and Merz, 1998)
have been used to characterize the efficiency of our
methods compared with other methods.
3.1 Performance Evaluation Criteria
It is now well-known that the traditional evaluation
criteria such as the sensitivity, precision, recall, speci-
ficity and accuracy are not longer appropriate for eval-
uating the performance of algorithms when there are
class imbalance problems, because the minority class
would be dominated by the majority class. For ex-
ample, in credit card fraud detection it is meaningless
to achieve high accuracy when a data set whose im-
balance ratio is 100, i.e., the number of majority class
examples (legitimate transactions) is 100 times that of
minority class examples (fraudulent transactions). An
algorithm that tries to maximize the accuracy may ob-
tain an accuracy of 99% just by predicting all the ex-
amples as majority class, though the accuracy seems
high, the predictor is useless since no fraudulent trans-
action will be detected.
Consequently, we adopt the AUC as the perfor-
mance evaluation measure, which has been proved to
be a reliable performance measure for class imbal-
ance problems (Fawcett, 2004). AUC is the area un-
der the receiver operating characteristic (ROC) curve,
where the ROC curve depicts the trade-off between
the benefits (t pr, true positive rate) and costs ( f pr,
false positive rate). AUC provides a single measure of
a method’s performance to evaluate which one is bet-
ter (the higher the value of AUC the better the perfor-
mance of the method). The AUC measure is achieved
by calculated the area under the ROC curve.
3.2 Implements and Parameters
Information about 11 UCI data sets is summarized in
Table 1: number of attributes (#Attribute), number of
examples (Size), number of minority class examples
(#Min), number of majority class examples (#Maj),
and imbalance ratio (IR). The data sets in Table 1
are ordered according to the ascending order of im-
balance ratio. The original Multi-class data sets of
UCI were revised to two-class imbalanced problems
by combining one or more classes into the minority
class and combining the remaining classes into the
majority class.
BIOINFORMATICS2015-InternationalConferenceonBioinformaticsModels,MethodsandAlgorithms
192
Table 1: Summary Description of the Imbalanced
Databases. #Attribute is the Number of Attributes, Size
is the Total Number of Examples, #Min and #Maj are the
Number of Minority Class Examples and Majority Class
Examples Respectively, and IR is the Imbalance Ratio.
Database #Attribute Size #Min #Maj IR
wdbc 30 569 212 357 1.7
ionosphere 33 351 126 225 1.8
pima 8 768 268 500 1.9
car 6 1728 518 1210 2.3
haberman 3 306 81 225 2.8
wpbc 33 198 47 151 3.2
mf-zernike 47 2000 200 1800 9.0
mf-morph 6 2000 200 1800 9.0
mf-kar 64 2000 200 1800 9.0
balance 5 625 49 576 11.8
abalone 8 4177 261 3916 15.0
We compared the performance of our proposed al-
gorithms with standard AdaBoost and EasyEnsemble
(Liu et al., 2009) in term of AUC. The EasyEnsemble
algorithm is also a an ensemble of ensembles. It uses
bagging as the main ensemble learning method and
trains each bag using AdaBoost. However, it only ap-
plies random undersampling method to deal with the
class imbalance problem. The number of boosting it-
erations T was set as 10 and the number of computing
workers (or the number of bags) M was selected as 4.
We adopted the decision tree (Mitchell, 1997) as the
weak learning algorithm. For each data set, we per-
form a 10-fold cross-validation for all methods. That
is, each data set was split into 10 folds, each fold con-
taining 10% of examples of the data set. For each
fold, algorithms were trained with the examples con-
tained in the remaining nine folds and then tested with
the current fold. The mean and standard deviation of
AUC of each method was calculated from the 10 re-
sults of this cross validation process.
3.3 Performances of Different Methods
We implemented four methods (AdaBoost,
EasyEnsemble, AdaBoost.BSR and AdaBoost.BSS)
on a single machine to compare their performance
in class imbalance problem. The mean and standard
deviation of AUC of all these methods are summa-
rized in Table 2. The mean and standard deviation
are presented above and below respectively. The
highest average AUC with its standard deviation of
each data set is marked bold. Table 2 shows that
EasyEnsemble, AdaBoost.BSR and AdaBoost.BSS
which are specially designed to deal with class
imbalance problem achieve better performance
than the standard AdaBoost. The proposed Ad-
aBoost.BSR and AdaBoost.BSS obtain the highest
average AUC on all the imbalanced data sets except
pima. Moreover, AdaBoost.BSS, which combines
the random undersampling method with the SMOTE
algorithm to cope with the class imbalance problem,
shows the superior performance with the increase
of imbalance ratio. This is probably due to that the
division mechanism of the the Balance-Sampling
algorithm can make the AdaBoost.BSR algorithm to
fully exploit useful information of the majority class
and SMOTE increases the ensemble diversity of it.
Table 2: AUC of the Compared Methods. The Mean and
Standard Deviation are Presented Above and Below Re-
spectively. The Highest Average AUC with Its Standard
Deviation of Each Data Set is Marked Bold.
AdaBoost EasyEnsemble AdaBoost.BSR AdaBoost.BSS
wdbc 0.9892 0.9914 0.9954 0.9870
0.0077 0.0083 0.0066 0.0134
ionosphere 0.9453 0.9739 0.9716 0.9709
0.0359 0.0240 0.0235 0.0398
pima 0.7514 0.8181 0.8339 0.8156
0.0293 0.0268 0.0362 0.0499
car 0.9999 0.9999 0.9999 0.9999
0.0002 0.0002 0.0002 0.0002
haberman 0.6617 0.6571 0.6812 0.6614
0.0901 0.1484 0.0842 0.0975
wpbc 0.6247 0.7387 0.7480 0.7573
0.1338 0.1739 0.0861 0.1388
mf-zernike 0.7957 0.9086 0.9011 0.9113
0.0389 0.0174 0.0213 0.0206
mf-morph 0.8824 0.9143 0.9216 0.9258
0.0350 0.0170 0.0159 0.0202
mf-kar 0.9915 0.9949 0.9956 0.9957
0.0119 0.0046 0.0039 0.0054
balance 0.6162 0.5779 0.6417 0.6707
0.1161 0.1399 0.0875 0.0873
abalone 0.8134 0.8728 0.8769 0.8815
0.0432 0.0314 0.0239 0.0259
4 CONCLUSION
We have developed two parallel ensemble meth-
ods (AdaBoost.BSR and AdaBoost.BSS) with the
purpose of trying to deal with the imbalanced big
data. We use bagging as the main ensemble learn-
ing method and train each bag using AdaBoost which
combines the advantages of both boosting and bag-
ging. In addition, the proposed Balance-Sampling
algorithm, which combines random undersampling
with random oversampling or the SMOTE algorithm,
is able to fully exploit useful information of the major-
ity class and increases the ensemble diversity. The ex-
perimental results indicate that our method can effec-
tively deal with the class imbalance problems, espe-
cially the data sets with higher imbalance ratio. Due
BalancedSamplingMethodforImbalancedBigDataUsingAdaBoost
193
to the algorithms’ parallel structure, our methods are
easier to be implemented in parallel. In the future, we
plan to implement our proposed methods on the im-
balanced big data sets in a parallel distributed MapRe-
duce framework to test their efficiency.
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