U0 vqmtq2otq=

International Journal of Science and Research (IJSR)
ISSN (Online): 2319-7064
Impact Factor (2012): 3.358
An Optimized Cost-Free Learning Using ABC-SVM
Approach in the Class Imbalance Problem
K. Sasikala, Dr. V. Anuratha
Tirupur (Dt), Tamil Nadu (St), India
Abstract: In this work, cost-free learning (CFL) formally defined in comparison with cost-sensitive learning (CSL). The primary
difference between them is that even in the class imbalance problem, a CFL approach provides optimal classification results without
requiring any cost information. In point of fact, several CFL approaches exist in the related studies like sampling and some criteria-based
approaches. Yet, to our best knowledge none of the existing CFL and CSL approaches is able to process the abstaining
classifications properly when no information is given about errors and rejects. Hence based on information theory, here we propose a
novel CFL which seeks to maximize normalized mutual information of the targets and the decision outputs of classifiers. With the help
of this strategy, we can manage binary or multi-class classifications with or without refraining. Important features are observed from the
new strategy. When the degree of class imbalance is changing, this proposed strategy could able to balance the errors and rejects
accordingly and automatically. A wrapper paradigm of proposed ABC-SVM (Artificial Bee Colony-SVM) is oriented on the evaluation
measure of imbalanced dataset as objective function with respect to feature subset, misclassification cost and intrinsic parameters of
SVM. The main goal of cost free ABC-SVM is to directly improve the performance of classification by simultaneously optimizing the best
pair of intrinsic parameters, feature subset and misclassification cost parameters. The obtained experimental results on various standard
benchmark datasets and real-world data with different ratios of imbalance show that the proposed method is effective in comparison with
commonly used sampling techniques.
Keywords: Classification, Class Imbalance, Cost-Free Learning, Cost-Sensitive Learning, artificial bee colony algorithm, Support vector
machine
1. Introduction
Recently, the class imbalance problem has been
recognized as a crucial problem in machine learning and
data mining [1] which occurs when the training data is not
evenly distributed among classes and is also especially
critical in many real applications such as credit card fraud
detection when fraudulent cases are rare or medical
diagnoses where normal cases are the majority. In these
cases, standard classifiers generally perform poorly. Also,
the classifiers usually tend to be overwhelmed by the
majority class and ignore the minority class examples with
most classifiers assuming an even distribution of examples
among classes and assume an equal misclassification cost.
Moreover, classifiers are typically designed to maximize
accuracy but that is not a good metric to evaluate
effectiveness in the case of imbalanced training data.
Hence, we need to improve traditional algorithms so as to
handle imbalanced data and choose other metrics to
measure performance instead of accuracy. Here we focus
our study on imbalanced datasets with binary classes.
Much work has been done in addressing the class
imbalance problem. These methods can be grouped in two
categories: the data perspective and the algorithm
perspective [2]. The methods with the data perspective re-balance
the class distribution by re-sampling the data
space either randomly or deterministically. The main
disadvantage of re-sampling techniques are that they may
cause loss of important information or the model over
fitting, since that they change the original data distribution.
The imbalanced learning problem in data mining has
attracted a significant amount of interest from the research
community and practitioners because real-world datasets
are frequently imbalanced containing a minority class with
relatively few instances when compared to the other
classes in the dataset. These standard classification
algorithms of literature which were used in supervised
learning have difficulties in correctly classifying the
minority class. Most of these algorithms assume a
balanced distribution of classes and equal misclassification
costs for each class. In addition, these algorithms are
designed to generalize from sample data and output the
simplest hypothesis that best fits the data.
This methodology is embedded as principle in the
inductive bias of many machine learning algorithms
including nearest neighbor, Decision Tree and Support
Vector Machine (SVM). Therefore, when they are used on
complex imbalanced data sets, these algorithms are
inclined to be overwhelmed by the majority class and
ignore the minority class causing errors in classification
for the minority class. Putting differently, standard
classification algorithms try to minimize the overall
classification error rate by producing a biased hypothesis
which regards almost all instances as the majority class.
Recent research on the class imbalance problem has
included studies on datasets from a wide variety of
contexts such as, information retrieval and filtering [3],
diagnosis of rare thyroid disease [4], text classification [5],
credit card fraud detection [6] and detection of oil spills
from satellite images [7]. Imbalance degree varies
depending on the context.
A cost-sensitive classifier tries to learn more
characteristics of samples with the minority class by
setting a high cost to the misclassification of a minority
class sample. It does not modify the data distribution.
Weiss [8] left the questions “why doesn’t the cost-sensitive
learning algorithm perform better given the
known draw-backs with sampling and are there ways to
improve the cost-sensitive learning algorithms
Volume 3 Issue 10, October 2014
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Paper ID: SEP14694 184
Licensed Under Creative Commons Attribution CC BY

effectiveness.” He pinpointed to improve the effectiveness
of cost sensitive learning algorithms by optimizing factors
which influence the performance of cost sensitive learning.
There are two challenges with respect to the training of
cost sensitive classifier. The misclassification costs play a
crucial role in the construction of a cost sensitive learning
model for achieving expected classification results.
Nevertheless, in many contexts of imbalanced dataset, the
costs of misclassification cannot be determined. Apart
from cost, intrinsic parameters and the feature set of some
sophisticated classifiers also influence the classification
performance. Moreover, these factors influence each other.
This is the first challenge. The other is the gap between the
measure of evaluation and the objective of training on the
imbalanced data [9]. Indeed, for evaluating the
performance of a cost-sensitive classifier on a skewed data
set, the overall accuracy is inapplicable. It is common to
employ other evaluation measures to monitor the balanced
classification ability, such as G-mean [10] and AUC [11].
However, these cost-sensitive classifiers measured by
imbalanced evaluation are not trained and updated with the
objective of the imbalanced evaluation. In order to achieve
good prediction performance, learning algorithms should
train classifiers by optimizing the concerned performance
measures [12].
In order to solve the challenges above, we propose a CFL
strategy in the class imbalance problem. Using normalized
mutual information (NI) as the learning target, we conduct
the learning from cost-insensitive classifiers. Therefore,
we are able to adopt conventional classifiers for simple
and direct implementations. The most advantage of this
strategy is its unique feature in classification scenarios
where one has no knowledge of costs. Simultaneously for
improving the performance of cost-free ABC-SVM
optimize the factors such as cost of misclassification,
intrinsic parameters and feature set of classifier.
The remainder of this paper is as follows. In section 2
related works is described. In section 3 proposed CF-ABC-SVM
discussed for class imbalance problem. In section 4
discussed the experimental results and conclusion is
described in section 5.
2. Related Work
When costs are unequal and unknown, Maloof [13] uses
ROC curve to show the performance of binary
classifications under different cost settings. To make fair
comparisons, an alternative to AUC is proposed to
evaluate different classifiers under the same cost ratio
distribution [14]. These studies can be viewed as
comparing classifiers rather than finding optimal operating
points. Cost curve [15] can be used to visualize optimal
expected costs over a range of cost settings, but it does not
suit multi-class problem. Zadrozny and Elkan [16] apply
least-squares multiple linear regression to estimate the
costs. The method requires cost information of the training
sets to be known. Cross validation [17] is proposed to
choose from a limited set of cost values, and the final
decisions are made by users.
There exist some CFL approaches in the class imbalance
problem. Various sampling strategies [18] try to modify
the imbalanced class distributions. Active learning [19] is
also investigated to select desired instances and the feature
selection techniques are applied to combat the class
imbalance problem for high-dimensional data sets.
Besides, ensemble learning methods are used to improve
the generalization of predicting the minority class. To
reduce the influence of imbalance, Hellinger distance is
applied to decision trees as a splitting criterion for its skew
insensitivity. And the recognition-based methods that train
on a single class are proposed as alternatives to the
discrimination-based methods.
However, all CFL methods above do not take abstaining
into consideration and may fail to process the abstaining
classifications. In regards to abstaining classification,
some strategies have been proposed for defining optimal
reject rules. Pietraszek [20] proposes a bounded-abstaintion
model with ROC analysis, and Fumera et al.
[21] seek to maximize accuracy while keeping the reject
rate below a given value. However, the bound information
and the targeted reject rate are required to be specified
respectively. When there is no prior knowledge of these
settings, it is hard to determine the values. Li and Sethi
[22] restrict the maximum error rate of each class, but the
rates may conflict when they are arbitrarily given.
Zhang et al [23] proposed a new strategy of CFL to deal
with the class imbalance problem. Based on the specific
property of mutual information that can distinguish
different error types and reject types, we seek to maximize
it as a general rule for dealing with binary/multiclass
classifications with/without abstaining. The challenge will
be a need of specific optimization algorithms for different
learning machines. Many sampling techniques have been
introduced including heuristic or non-heuristic
oversampling, undersampling and data cleaning rules such
as removing “noise” and “borderline”. These works focus
on data-level techniques whereas, other researchers
concentrate on changing the classifier internally as for
example SVM that is to deal with class imbalance;
Whereas uses ensemble learning to deal with class
imbalance while combines undersampling with ensemble
methods; focuses on incorporating different re-balance
heuristics to SVM to tackle the problem of class imbalance
while incorporate SVM into a boosting method.
These all literature studies introduced a test strategy which
determines how unknown attributes are selected to
perform test on in order to minimize the sum of the
misclassification costs and test costs. Furthermore, applied
synthetic minority oversampling technique (SMOTE) to
balance the dataset at first and then built the model using
SVM with different costs proposed applied some common
classifiers (e.g. C4.5, logistic regression, and Naive Bayes)
with sampling techniques such as random oversampling,
random undersampling and condensed nearest neighbor
rule, Wilson’s edited nearest neighbor rule, Tomek’s link,
and SMOTE. In different to the literature, rather than
focusing only on data sampling or CSL, here we propose
using both techniques. In addition to that, we also do not
assume a fixed cost ratio and we neither set the cost ratio
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by inverting the ratio of prior distributions between
minority and majority class. Here instead, optimize the
cost ratio locally.
3. Dealing with Class Imbalance with ABC-SVM
On dealing with imbalanced datasets, literature researchers
focused on the data level and the classifier level. At the
data level, the common task is the modification of the class
distribution whereas at the classifier level many techniques
were introduced such as manipulating classifiers
internally, ensemble learning, one-class learning and CFL.
1.1 Cost-Free SVM
Support Vector Machines (SVM), which has strong
mathematical foundations based on statistical learning
theory that has been successfully adopted in various
classification applications. SVM aims maximizing a
margin in a hyper plane separating classes. However, it is
overwhelmed by the majority class instances in the case of
imbalanced datasets because the objective of regular SVM
is to maximize the accuracy. In order to provide different
costs associated with the two different kinds of errors,
cost-sensitive SVM (CF-SVM) [15] is a good solution.
CF-SVM is formulated as follows:
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min ଵ
ଶ
‖ݓ‖ଶ + ܥା Σ௜;௝೟ୀାଵ ߦ௜ + ܥି Σ௝;௬ೕୀିଵ ߦ௜
st ݕ௜ሾሺݓ் ݔ௜ሻ + ܾሿ ≥ 1 − ߦ௜ ∀ ݅ = 1, ܮ, . . ݊ ߦ௜ ≥ 0
where the ܥା is the higher misclassification cost of the
positive class that is the primary interest, where ܥ— is the
lower misclassification cost of the negative class. Using
the different error cost for the positive and negative
classes, this SVM hyper plane could be pushed away from
the positive instances. In this paper, we fix ܥ— = ܥ and
ܥା = ܥ × ܥ௥௙ , where C and ܥ௥௙ are respectively the
regularization parameter and the ratio of misclassification
cost. On the construction of cost sensitive SVM, this
misclassification cost parameter plays an indispensable
role. In general, the Radial Basis Function (RBF kernel) is
a reasonable first choice for the classification of the
nonlinear datasets, as it has fewer parameters (γ).
1.2 Optimized cost free SVM by measure of
imbalanced data
SVM tries to minimize the regularized hinge loss; it is
driven by an error based objective function. Yet, the
obtained overall accuracy is not an appropriate evaluation
measure for imbalanced data classification. Finally, there
is an inevitable gap between the evaluation measure by
which the classifier is to be evaluated and the objective
function based on which the classifier is trained. The
classifier for imbalanced data learning should be driven by
more appropriate measures. We inject the appropri-ate
measures into the objective function of the classifier in the
training with ABC. The common evaluation for
imbalanced data classification is G-mean and AUC.
However for many classifiers, yet the learning process is
still driven by error based objective functions. In this paper
we explicitly treat the measure itself as the objective
function when training the cost sensitive learning. Here,
we designed a measure based training framework for
dealing with imbalanced data classification issues. A
wrapper paradigm proposed that discovers the amount of
re-sampling for a dataset based on optimizing evaluation
functions like the f-measure, and AUC. To date, there is no
research about training the cost sensitive classifier with
measure based objective functions. This is one important
issue that hinders the performance of cost-sensitive
learning.
Another important issue of applying the cost-sensitive
learning algorithm to the imbalanced data is that the cost
matrix is often unavailable for a problem domain. The
misclassification cost, especially the ratio misclassification
cost, plays a crucial role in the construction of a cost
sensitive approach; the knowledge of misclassification
costs is required for achieving expected classification
result. However, the values of costs are commonly given
by domain experts. They remain unknown in many
domains where it is in fact difficult to specify the cost ratio
information precisely. Also, it is not the correct method to
set the cost ratio to the inverse of the imbalance ratio (the
number of majority in-stances divided by the number of
minority instances); especially it is not accurate for some
classifier such as SVM. Heuristic approaches were used
search the optimal cost matrix in some of the cost sensitive
learning such as Genetic Algorithm or grid search to find
the optimal cost setup. Feature subset selection and the
intrinsic parameters of the classifier have a significant
bearing on the performance, apart from the ratio
misclassification cost information. These both factors are
not only important for classification of imbalanced data,
but also applicable for any kind of classification. The
technique, feature selection is used for selecting a subset
of discriminative features for building robust learning
models by removing most irrelevant and redundant
features from the data. Furthermore, this advanced optimal
feature selection can concurrently achieve good accuracy
and dimensionality reduction.
Unfortunately, the imbalanced data distributions are often
accompanied by high dimensionality in real-world datasets
such as bio-informatics, text classification and CAD
(Computer Aided Detection). It is important to select
features that can capture the high skew in the class
distribution. Furthermore, proper intrinsic parameter
setting of classifiers like regularization of cost parameter
and the kernel functional parameter of SVM can improve
the classification performance. It is necessary to use the
grid search to optimize the kernel parameter and regulation
parameters. Also, these three factors influence each other.
Thus, we obtain the optimal ratio of cost of
misclassification, feature subset selection and intrinsic
parameters must occur simultaneously.
Based on the reasons above, our specific goal is to devise a
strategy to automatically determine the optimal factors
during training of the cost sensitive classifier oriented by
the imbalanced evaluation criteria (G-mean and AUC). For
binary class classification, there is only one parameter
called cost parameter i.e., the relative cost information,

known as ratio misclassification cost factor Crf. Since the
RBF kernel is selected for the cost sensitive SVM, γ and C
are the parameters to be optimized. We need to combine
the discrete and continuous values in the solution
representation since the costs and parameters we intend to
optimize are continuous while the feature subset is discrete
as like each and every feature is represented by a 1 or 0 for
whether it is selected or not. In our proposed method, the
food source (solution) is randomly generated in the initial
process. Then, each solution is evaluated through SVM
classifier. The solving of SVM is generally a quadratic
programming (QP) problem; sequential minimal
optimization (SMO) will be applied in this study to
optimize the computation time of training period of SVM.
SMO divides the large QP problem into series of smallest
possible QP problem to avoid the intensive time and
memories required. For this study, the radial basis function
(RBF) is used as the kernel function of non-linear SVM
classifier to learn and recognize pattern of input data from
the training set. The equation of RBF function is defined
as
(1)
where r is a kernel parameter in RBF function. Then, a
testing set is used to determine the classification accuracy
for the input dataset. The fitness value is obtained by the
classification accuracy of this testing dataset. For a small-and
medium-sized data, the accurate value can be
estimated by using the 10-fold cross-validation method.
The method will randomly separate data into 10 subsets;
one subset is used as a testing set while the remaining nine
subsets are used as training sets. The process will be
performed for 10 times in total. As a result, each subset
will be used once as a validation or testing set. The
accuracy of classification will be obtained from the
average of all correctness values from 10 rounds. For the
large-sized data, the holdout method is applied. This
method divides the data into two parts for construction
training and testing models. Each food source is modified
based on the process of updating feasible solution by
employed bees as expressed in the equation (2) where Φ is
a random number in the range between [-1,1], negative one
and one.
The equation (2) returns a numerical number of a new
candidate solution vij from their current food source xij
and their neighboring food source xkj. However, for
dimension reduction these solutions must be binary
numbers. Thus, this numeric solution must be converted
into either 0 or 1 by using equation (3) and (4) as follows:
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ܭ൫ݔ௜ , ݔ௝൯ = ݁ି௥൫௫೔,௫ೕ൯మ
ݒ௜௝ = ݔ௜௝ + Φሺx୧୨ − x୩୨ሻ (2)
ܵ൫ݒ௜௝൯ = ଵ
ଵା௘షೡ೔ೕ (3)
݂݅ ቀݎܽ݊݀ ൏ ܵ൫ݒ௜௝ ൯ቁ ݐ݄݁݊ ݒ௜௝ = 1; ݈݁ݏ݁ ݒ௜௝ = 0 (4)
The equation (3) is a sigmoid limiting function into the
interval [0.0, 1.0]. Then, a random number between range
[0.0, 1.0], rand, is used to determine the binary value of
the solution in the equation (4). The new candidate
solution must be evaluated with SVM classifier. If the new
fitness value is better than the current one, the employed
bees will replace its solution with this new candidate
solution; otherwise, the new candidate solution will be
ignored. Onlooker bees will select a food source according
to the calculated probability of each food sources based on
the equation (5), once after employed bees share
information of their solutions.
ܲ௜ = ௙௜௧೔
ಿ
೔సభ
Σ ௙௜௧೔
(5)
where ܲ௜ is the probability value of the solution i, N is the
number of all solutions, and ݂݅ݐ௜ is the fitness value of the
solution i. Thus, the solution with higher fitness value will
have greater opportunity to be selected by the onlooker
bees. After the onlooker bees select their desirable food
source, the bees will perform the process of updating
feasible solution similar to employed bees. The whole
processes will be repeated until the termination criterion is
reached. The dimension reduction process of ABC-SVM is
summarized as follows:
Figure 1: The flowchart of ABC-SVM method

4. Experimental Results and Discussion
1.3 Dataset Description
To evaluate the classification performance of our proposed
method in different tasks of classification and to compare
with other methods specifically devised for imba-lanced
data, we tried several datasets from the UCI database. We
used all available datasets from the combined sets used.
This also ensures that we did not choose only the datasets
on which our method performs better. The minority class
label (+) is indicated in Table 1 and the chosen datasets
contains diversity in the number of attributes and
imbalance ratio. Also, these shown datasets have both
continuous and categorical attributes of data. All the
experiments are conducted by 10-fold cross-validation.
Table 1: The data sets used for experimentation the
dataset name is appended with the label of the minority
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class (+)
Dataset Instances Features Class Imbalance
Hepatitis (1) 155 19 1:4
Glass(7) 214 9 1:6
Segment(1) 2310 19 1:6
Anneal(5) 898 38 1:12
Soybean(12) 683 35 1:15
The comparison is conducted between our method and the
other state-of-the-art imba-lanced data classifiers, such as
the random under-sampling (RUS), SMOTE,
SMOTEBoost, and SMOTE combined with asymmetric
cost classifier. The re-sampling rate of under-sampling
algorithm such as the SMOTE and SMOTEBoost is
unknown. In order to compare equally, in our experiments,
no matter whether it is under-sampling or over-sampling
method, we used the evaluation measure as the
optimization objective of the re-sampling method to search
the optimal re-sampling level. The steps of both increment
and decrement are set at 10%. This is a greedy search kind
of approach which repeats the process greedily, upto no
performance gains are observed.
Then the optimal rate of resampling is decided in an
iterative fashion according to the evaluation metrics.
Hence in the each fold, these data of training set is
separated into training subset and validating subset for
searching the appropriate rate parameters. The evaluation
metrics are also used with the G-mean and AUC. For the
CS-SVM with SMOTE, for each search of re-sampling,
the optimal misclassification cost ratio is determined by
searching under the evaluation measure guiding under the
current over-sampling level of SMOTE.
1.4 Execution Time Comparison
This graph contains execution time of planned and existing
system. The execution time of existing method is
incredibly high compared with the planned system. The
initial purpose of CF-ABC-SVM approach is there
employing a screening methodology it'll be useful for
mechanically effort class imbalance problem. This is
shown in Fig.2. From the results it is observed that the
proposed work takes less computational time to solve the
class imbalance problem.
Figure 2: Execution Time Comparison
1.5 Accuracy
This graph contains execution time of planned and existing
system. The accuracy of proposed system is incredibly
high compared with the planned system. The initial
purpose of CF-ABC-SVM approach is there employing a
screening methodology it'll be useful for mechanically
effort class imbalance problem. This is shown in Fig.3.
From the results it is observed that the proposed work
takes less computational time to solve the class imbalance
problem.
Figure 3: Accuracy Comparison
5. Conclusion
Learning with class imbalance is a challenging task. We
propose a wrapper paradigm oriented by the evaluation
measure of imbalanced dataset as objective function with
respect to cost of misclassification, selection of feature
subset and intrinsic parameters of SVM. Our measure
oriented framework could wrap around an existing cost-sensitive
classifier. The proposed method has been
validated on some benchmark imbalanced data and real-world
application. The obtained experimental results in
this study have demonstrated that the proposed framework
provides a very competitive solution to other existing
state-of-the-arts methods, in terms of optimization of G-mean
and AUC for conflicting imbalanced classification
problems. These experimental results confirm the
advantages of our approach that shows the promising

perspective and new understanding of cost sensitive
learning. In the future research, we will extend the
framework to the imbalanced multiclass data
classification.
References
[1] Chawla, N.V., Japkowicz, N.& Kolcz, A. (2004):
Editorial: special issue on learning from imbalanced
data sets. SIGKDD Explorations Special Issue on
Learning from Imbalanced Datasets 6 (1):1-6.
[2] Kotsiantis, S., Kanellopoulos, D. & Pintelas, P.
(2006): Handling imbalanced datasets: A review.
GESTS International Transactions on Computer
Science and Engineering:25-36.
[3] Lewis, D & Catlett, J.(1994). Heterogeneous
uncertainty sampling for supervised learning. In
Cohen, W. W. & Hirsh, H. (Eds.), Proceedings of
ICML-94, 11th International Conference on Machine
Learning, (pp. 148-156)., San Francisco. Morgan
Kaufmann
[4] Murphy, P. & Aha, D.(1994). UCI repository of
machine learning databases. University of California-
Irvine, Department of Information and Computer
Science.
[5] Chawla, N.V., Bowyer, K.W., Hall, L.O., &
Kegelmeyer, W.P.(2002). SMOTE: Synthetic
Minority Over-sampling Technique. Journal of
Artificial Intelligence and Research 16, 321-357.
[6] Wu, G. & Chang, E. (2003). Class-Boundary
Alignment for Imbalanced Dataset Learning. In ICML
2003 Workshop on Learning from Imbalanced Data
Sets ΙΙ, Washington, DC.
[7] Kubat, M., Holte, R., & Matwin, S.(1998). Machine
learning for the detection of oil spills in satellite radar
images. Machine Learning, 30, 195-215
[8] Weiss G., McCarthy K., Zabar B. (2007): Cost-sensitive
learning vs. sampling: Which is Best for
Handling Unbalanced Classes with Unequal Error
Costs? IEEE ICDM, pp. 35–41.
[9] Yuan, B. & Liu, W.H. (2011): A Measure Oriented
Training Scheme for Imbalanced Clas-sification
Problems. Pacific-Asia Conference on Knowledge
Discovery and Data Mining Workshop on
Biologically Inspired Techniques for Data Mining.
pp:293–303.
[10] Akbani, R., Kwek, S. & Japkowicz, N. (2004):
Applying support vector machines to imba-lanced
datasets. European conference on machine learning.
[11] Chawla, N.V., Cieslak, D.A., Hall, L. O. & Joshi, A.
(2008): Automatically countering im-balance and its
empirical relationship to cost. Utility-Based Data
Mining: A Special issue of the International Journal
Data Mining and Knowledge Discovery.
[12] Li, N., Tsang, I., Zhou, Z. (2012): Efficient
Optimization of Performance Measures by Classifier
Adaptation. IEEE Transactions on Pattern Analysis
and Machine Intelligence. Volume: PP , Issue: 99,
Page(s): 1.
[13] M.A. Maloof, “Learning When Data Sets are
Imbalanced and When Costs are Unequal and
Unknown,” Proc. Workshop on Learning from
Imbalanced Data Sets II. Int’l Conf. Machine
Learning, 2003
[14] D.J. Hand, “Measuring Classifier Performance: A
Coherent Alternative to the Area under the ROC
Curve,” Machine Learning, vol. 77, no. 1, pp. 103-
123, Oct. 2009
[15] C.C. Friedel, U. R¨ uckert, and S. Kramer, “Cost
Curves for Abstaining Classifiers,” Proc. Workshop
on ROC Analysis in Machine Learning. Int’l Conf.
Machine Learning, 2006.
[16] B. Zadrozny and C. Elkan, “Learning and Making
Decisions When Costs and Probabilities are Both
Unknown,” Proc. ACM SIGKDD Int’l Conf.
Knowledge Discovery and Data Mining, pp. 204-213,
2001.
[17] Y. Zhang and Z.-H. Zhou, “Cost-Sensitive Face
Recognition,” IEEE Trans. Pattern Analysis and
Machine Intelligence, vol. 32, no. 10, pp. 1758-1769,
Oct. 2010.
[18] M. Wasikowski and X.-W. Chen, “Combating the
Small Sample Class Imbalance Problem Using
Feature Selection,” IEEE Trans. Knowledge and Data
Eng., vol. 22, no. 10, pp. 1388-1400, Oct. 2010.
[19] S. Wang and X. Yao, “Relationships between
Diversity of Classification Ensembles and Single-
Class Performance Measures,” IEEE Trans.
Knowledge and Data Eng., vol. 25, no. 1, pp. 206-
219, Jan. 2013.
[20] T. Pietraszek, “Optimizing Abstaining Classifiers
using ROC Analysis,” Proc. Int’l Conf. Machine
Learning, pp. 665-672, 2005.
[21] G. Fumera, F. Roli, and G. Giacinto, “Reject Option
with Multiple Thresholds,” Pattern Recognition, vol.
33, no. 12, pp. 2099-2101, 2000.
[22] M. Li and I.K. Sethi, “Confidence-Based Classifier
Design,” Pattern Recognition, vol. 39, no. 7, pp. 1230-
1240, Jul. 2006.
[23] Xiaowan Zhang and Bao-Gang Hu, Senior Member,
‘A New Strategy of Cost-Free Learning in the Class
Imbalance Problem’ IEEE 1041-4347 (c) 2013 IEEE
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