Graphics Reference
In-Depth Information
n
1
n
2
σ
A
=+
1
(
v
i
−
A
)
.
(3.12)
i
=
A variation of the z-score normalization, described in [
15
], uses the mean absolute
deviation
s
A
of
A
instead of the standard deviation. It is computed as
n
1
n
s
A
=
1
|
v
i
−
A
|
.
(3.13)
i
=
As a result the z-score normalization now becomes:
v
−
A
v
=
.
(3.14)
s
A
An advantage of the
s
A
mean absolute deviation is that it is more robust to outli
ers
than the standard deviation
σ
A
as the deviations from the mean calculated by
|
v
i
−
A
|
are not squared.
3.4.3 Decimal Scaling Normalization
A simple way to reduce the absolute values of a numerical attribute is to normalize
its values by shifting the decimal point using a power of ten division such that
the maximum absolute value is always lower than 1 after the transformation. This
transformation is commonly known as decimal scaling [
15
] and it is expressed as
v
10
j
,
v
=
(3.15)
w
−
max
A
<
where
j
is the smallest integer such that
ne
1.
3.5 Data Transformation
In the previous Sect.
3.4
we have shown some basic transformation techniques to
adapt the ranges of the attributes or their distribution to a DM algorithm's needs. In
this section we aim to present the process to create new attributes, often called trans-
forming the attributes or the attribute set. Data transformation usually combines the
original raw attributes using different mathematical formulas originated in business
models or pure mathematical formulas.
