Database Reference
In-Depth Information
Table 4. Early Classification. Results (error rates) for the different data sets using
the different literals.
Data set
Percentage
Point
Relative
Always/
True
Interval
sometimes
percentage
CBF
60
4.51
4.65
2.63
1.39
0.88
CBF
80
4.26
2.70
2.01
0.50
0.75
CBF-Var
60
4.11
1.86
3.12
1.87
1.61
CBF-Var
80
3.49
1.87
2.75
1.25
1.00
Control
60
42.17
17.33
30.17
35.00
34.33
Control
80
11.67
3.50
1.67
1.17
1.00
Control-Var
60
22.50
20.67
20.33
19.00
17.17
Control-Var
80
13.00
7.17
5.00
5.33
5.00
Trace
60
83.33
32.00
55.48
47.73
37.10
Trace
80
70.95
0.45
5.45
7.68
0.63
Gloves
60
5.00
4.00
4.50
3.00
1.50
Gloves
80
5.00
4.00
4.50
2.50
1.50
literals. Table 3 also shows for these data sets the obtained results using
more iterations.
An interesting issue of these results is that the error rate achieved using
point based literals are always the worst; a detailed study of this topic
for fixed length time series can be found in [Rodriguez
et al.
(2001)]. The
obtained results for the setting named
Interval
are the better or very close
to the better results. The comparison between relative and region based
literal clearly indicates that its adequacy depends on the data set.
Table 4 shows some results for early classification. The considered
lengths are expressed in terms of the percentage of the length of the longest
series in the data set. The table shows early classification results for 60%
and 80%. Again, the usefulness of interval literals is clearly confirmed.
The rest of this section contains a detailed discussion for each data set,
including its description, the results for boosting point based and interval
based literals and another known results for the data set.
6.1.
CBF (Cylinder, Bell and Funnel)
This is an artificial problem, introduced in [Saito (1994)]. The learning task
is to distinguish between three classes: cylinder (
c
), bell (
b
) or funnel (
f
).
Examples are generated using the following functions:
c
(
t
)=(6+
η
)
· χ
[
a,b
]
(
t
)+
ε
(
t
)
,
b
(
t
)=(6+
η
)
· χ
[
a,b
]
(
t
)
·
(
t − a
)
/
(
b − a
)+
ε
(
t
)
,
f
(
t
)=(6+
η
)
· χ
[
a,b
]
(
t
)
·
(
b − t
)
/
(
b − a
)+
ε
(
t
)
