Graphics Reference
In-Depth Information
Table 3.1
Applying quadratic transformations to identify the implicit conic figure
A
1
A
2
A
3
A
4
A
5
A
6
Z
Sign
Conic
1
0
42
2
34
−
33
−
168
−
Hyperbola
−
5
−
64
−
68
0
0
29
0
0
Parabola
88
−
6
−
17
−
79
97
−
62
6,020
+
Ellipse
30
0
0
−
53
84
−
14
0
0
Parabola
1
19
−
57
99
38
51
589
+
Ellipse
15
−
39
35
98
−
52
−
40
−
579
−
Hyperbola
Although the above given example indicates that transformations are necessary
for knowledge discovery in certain scenarios, we usually do not have any clue on
how such transformation can be found and when should them be applied. As [
24
]
indicates, the best source for obtaining the correct transformation is usually the expert
knowledge. Sometimes the best transformation can be discovered by brute force (see
Sect.
3.5.4
).
3.5.3 Non-polynomial Approximations of Transformations
Sometimes polynomial transformations, including the lineal and quadratic ones, are
not enough to create new attributes able to facilitate the KDD task. In other words,
each problem requires its own set of transformations and such transformations can
adopt any form. For instance, let us consider several triangles in the plane described
by the
coordinates of their vertices as shown in Table
3.2
. Considering only
these attributes does not provide us any information about the relationship of the
triangles, but by computing the length of the segments given by:
(
X
,
Y
)
=
(
X
1
−
X
2
)
2
+
(
Y
1
−
Y
2
)
2
A
(3.21)
2
2
B
=
(
X
2
−
X
3
)
+
(
Y
2
−
Y
3
)
(3.22)
2
2
C
=
(
X
1
−
X
3
)
+
(
Y
1
−
Y
3
)
(3.23)
we can observe that all the segments are of the same length. Obtaining this con-
clusions from the original attributes was impossible and this example is useful to
illustrate that some specific and non-polynomial attribute transformations are needed
but they are also highly dependent of the problem domain. Selecting the appropriate
transformation is not easy and expert knowledge is usually the best alternative to do
so.
