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Once clusters are formed the postprocessing starts. Initially clusters are projected
on all attributes. Then the resulting intervals are merged to reduce the number of
intervals and, at the same time, preserving consistency. Merging of intervals begins
from
safe merging
, where, for each attribute, neighboring intervals labeled by the
same decision value are replaced by their union. The next step of merging intervals
is based on checking every pair of neighboring intervals whether their merging will
result in preserving consistency. If so, intervals are merged permanently. If not, they
are marked as un-mergeable.
Thus, all data sets used for experiments were complete and symbolic.
Our experiments were conducted on a machine with 34GB of RAMwith Intel(R)
Xeon Processor X5650 (12MB cache, 2.66GHz, 6 Cores) under Fedora 17 Linux
operating system.
In our experiments, for any data set, for both algorithms, LEM1 and LEM2,
the same ten pairs of training and testing data sets were used during ten-fold cross
validation. Hence, for any fold, the same training data sets were used for induction
and the same testing data sets were used for computing an error rate. Additionally, the
same LERS classificationmethod was used for computing errors. The only difference
was in different strategies of rule induction used in LEM1 and LEM2. Additionally,
for both algorithms, we used only
certain
rule sets for inconsistent data sets. Results
of our experiments are presented in Tables
8.7
,
8.8
and
8.9
.
Table 8.7
Results of
experiments—an error rate
Data set
LEM1 (%)
LEM2 (%)
Australian Credit Approval
21.74
16.67
Breast Cancer—Slovenia
36.71
34.62
Breast Cancer—Wisconsin
19.68
22.24
Bupa Liver Disorders
36.52
36.81
Glass
33.18
31.31
Hepatitis
21.94
16.77
Image segmentation
17.62
18.10
Iris
3.33
4.67
Lymphography
31.08
18.24
Pima
33.46
30.73
Postoperative patients
41.11
35.36
Soybean
23.45
14.98
Primary tTumor
60.18
62.64
Wine Recognition
8.43
5.06
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