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In-Depth Information
to partial data. Regarding dynamic discretizers, they find the cut points in internal
operations of a DM algorithm, so they never gain access to the full data set.
•
Direct versus Incremental:
Direct discretizers divide the range into
k
intervals
simultaneously, requiring an additional criterion to determine the value of
k
.They
do not only include one-step discretization methods, but also discretizers which
perform several stages in their operation, selecting more than a single cut point at
every step. By contrast, incremental methods begin with a simple discretization
and pass through an improvement process, requiring an additional criterion to
know when to stop it. At each step, they find the best candidate boundary to be
used as a cut point and afterwards the rest of the decisions are made accordingly.
Incremental discretizers are also known as hierarchical discretizers [
9
]. Both types
of discretizers are widespread in the literature, although there is usually a more
defined relationship between incremental and supervised ones.
•
Evaluation Measure:
This is the metric used by the discretizer to compare two
candidate schemes and decide which is more suitable to be used. We consider five
main families of evaluation measures:
-
Information:
This family includes
entropy
as the most used evaluation measure
in discretization (MDLP [
41
], ID3 [
92
], FUSINTER [
126
]) and other derived
information theory measures such as the
Gini index
[
66
].
-
Statistical:
Statistical evaluation involves the measurement of dependency/
correlation among attributes (Zeta [
58
], ChiMerge [
68
], Chi2 [
76
]), probability
and bayesian properties [
119
] (MODL [
16
]), interdependency [
70
], contingency
coefficient [
106
], etc.
-
Rough Sets:
This group is composed of methods that evaluate the discretization
schemes by using rough set measures and properties [
86
], such as lower and
upper approximations, class separability, etc.
-
Wrapper:
This collection comprises methods that rely on the error provided by
a classifier that is run for each evaluation. The classifier can be a very simple
one, such as a majority class voting classifier (Valley [
108
]) or general classifiers
such as Naïve Bayes (NBIterative [
87
]).
-
Binning:
This category refers to the absence of an evaluation measure. It is the
simplest method to discretize an attribute by creating a specified number of bins.
Each bin is defined as a priori and allocates a specified number of values per
attribute. Widely used binning methods are EqualWidth and EqualFrequency.
9.3.1.2 Other Properties
We can discuss other properties related to discretization which also influence the
operation and results obtained by a discretizer, but to a lower degree than the
characteristics explained above. Furthermore, some of them present a large variety
of categorizations and may harm the interpretability of the taxonomy.
•
Parametric versus Non-Parametric:
This property refers to the automatic determi-
nation of the number of intervals for each attribute by the discretizer. A nonpara-
