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methods estimate the MVs using such relationships and can afford improvements in
the performance of the classifiers. Hence the highest values of average Mui ratios
could be related to those methods which can obtain better estimates for the MVs, and
maintaining the relationship degree between the class labels and the isolated input
attributes. It is interesting to note that when analyzing the Mui ratio, the values do
not appear to be as highly data dependant as Wilson's noise ratio, as the values for
all the data sets are more or less close to each other.
If we count the methods with the lowest Wilson's noise ratios in each data set
in Table
4.2
, we find that the CMC method is first, with 12 times being the lowest
one, and the EC method is second with 9 times being the lowest one. If we count the
methods with the highest MI ratio in each data set, the EC method has the highest
ratio for 7 data sets and is therefore the first one. The CMC method has the highest
ratio for 5 data sets and is the second one in this case. Immediately the next question
arises: are these methods also the best for the performance of the learning methods
applied afterwards? We try to answer this question in the following.
4.6.2 Best Imputation Methods for Classification Methods
Our aim is to use the same imputation results as data sets used in the previous
Sect.
4.6.1
as the input for a series of well known classifiers in order to shed light on
the question “which is the best imputation method?”. Let us consider a wide range
of classifiers grouped by their nature, as that will help us to limit the comparisons
needed to be made. We have grouped them in three sub-categories. In Table
4.3
we summarize the classification methods we have used, organized in these three
categories. The description of the former categories is as follows:
•
The first group is the
Rule Induction Learning
category. This group refers to
algorithms which infer rules using different strategies.
•
The second group represents the
Black Box Methods
. It includes ANNs, SVMs
and statistical learning.
•
The third and last group corresponds to the
Lazy Learning
(LL) category. This
group incorporates methods which do not create any model, but use the training
data to perform the classification directly.
Somemethods do not workwith numerical attributes (CN2, AQandNaïve-Bayes).
In order to discretize the numerical values, we have used the well-known discretizer
proposed by [
28
]. For the SVM methods (C-SVM,
-SVM and SMO), we have
applied the usual preprocessing in the literature to these methods [
25
]. This pre-
processing consists of normalizing the numerical attributes to the
ν
range, and
binarizing the nominal attributes. Some of the presented classification methods in the
previous section have their own MVs treatment that will trigger when no imputation
is made (DNI): C4.5 uses a probabilistic approach to handling MVs and CN2 applies
the MC method by default in these cases. For ANNs [
24
] proposed to replace MVs
with zero so as not to trigger the corresponding neuron which the MV is applied to.
[
0
,
1
]
