CLASS IMBALANCE LEARNING METHODS FOR SUPPORT VECTOR MACHINES - Imbalanced Learning: Foundations, Algorithms, and Applications - page 85

misclassifications should be reduced. When the dataset is imbalanced, the density
of majority class examples would be higher than the density of minority class
examples even around the class boundary region, where the ideal hyperplane
would pass through (throughout this chapter we consider the majority class as
the negative class and the minority class as the positive class). It is also pointed
out in [9] that the low presence of positive examples makes them appear further
from the ideal class boundary than the negative examples. As a consequence,
in order to reduce the total number of misclassifications in SVM learning, the
separating hyperplane can be shifted (or skewed) toward the minority class. This
shift/skew can cause the generation of more false negative predictions, which
lowers the model's performance on the minority positive class. When the class
imbalance is extreme, the SVMs could produce models having largely skewed
hyperplanes, which would even recognize all the examples as negatives [10].

5.3.2 The Imbalanced Support-Vector Ratio

Wu and Chang [9] have experimentally identified that as the training data gets
more imbalanced, the ratio between the positive and negative support vectors also
becomes more imbalanced. They have hypothesized that as a result of this imbal-
ance, the neighborhood of a test instance close to the boundary is more likely
to be dominated by negative support vectors, and hence the decision function
is more likely to classify a boundary point as negative. However, Akbani et al.
[10] have argued against this idea by pointing out that because of the constraint

i = 1 y i α i

0 (given in Eq. 5.4), α i of each positive support vector, which are
less in numbers than the negative support vectors, must be larger in magnitude
than the α i values associated with the negative support vectors. These α i act as
weights in the final decision function (Eq. 5.9), and hence larger α i in the pos-
itive support vectors receive higher weights than the negative support vectors,
which can reduce the effect of imbalance in support vectors up to some extent.
Akbani et al. [10] have further argued that this could be the reason why SVMs
do not perform very badly, as compared to other machine learning algorithms
for moderately skewed datasets.
In the remaining sections of this chapter, we review the methods found in the
literature to handle the class imbalance problem for SVMs. These methods have
been developed as both data preprocessing methods (called external methods )
and algorithmic modifications to the SVM algorithm (called internal methods ).

=

5.4 EXTERNAL IMBALANCE LEARNING METHODS FOR SVMs:
DATA PREPROCESSING METHODS

5.4.1 Resampling Methods

All the data preprocessing methods discussed in the other chapters of this topic
can be used to balance the datasets before training the SVM models. These