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The random feature subset selection of a random size is also implemented inside
the base classifier. This takes place for each rule and for each term expansion of
that rule. The resulting base classifier has been termed 'R-PrismTCS', where the
'R' stands for the 'Random' components in the base classifier (random feature
subset selection for each rule term and bagging).
Algorithm
1
shows the steps of R-PrismTCS with the exception of J-pruning.
F
denotes the total number of features,
D
is the original training data and
rule set
is an initially empty set of classification rules. The operation
rule.add
Term
(
A
x
) adds attribute value pair
A
x
as a rule term to
rule
and the operation
rule set.add
(
rule
) adds
rule
to
rule set
.Instep2foreach
A
x
the conditional
probability
p
(
class
=
i|A
x
) is calculated, which is the probability with which
A
x
covers the target class
i
.
Algorithm 1
: R-PrismTCS Algorithm
D
= build random sample with replacement from
D
;
D
=
D
;
Step 1: find class
i
that has the fewest instances in
D
;
rule = new empty rule for target class
i
;
Step 2: generate a feature subset
f
of size
m
,where(
F>m>
0);
calculate for each
A
x
in
fp
(
class
=
i|A
x
);
Step 3: select the
A
x
with the maximum
p
(
class
=
i|A
x
);
rule.addTerm
(
A
x
);
delete all instances in
D
that do not cover rule;
Step 4: repeat 2 to 3 for
D
until
D
only contains instances of target class
i
;
Step 5:
rule set.add
(
rule
);
create a new
D
that comprises all instances of
D
except those that are
covered by all rules induced so far;
Step 6: IF (number of instances
D
>
1)
{
repeat steps 1 to 6
}
;
Figure
1
shows the conceptual architecture of Random Prism. Each R-Prism
TCS base classifier is induced on a training sample of size
N
from the training
data, where
is also the size of the training data. This sample is drawn using
random sampling with replacement. This statistically results in samples that
contain 63.2 % of the original instances, some of them drawn multiple times.
The remaining 36.8 % of the instances that have not been drawn are used as
validation data to estimate the individual R-PrismTCS classifier's predictive
accuracy ranging from 0 to 1. We call this accuracy the classifier's weight. The
individual classifier's weights are then used to perform weighted majority voting
on unlabelled data instances. The weights can also be used to filter base classi-
fiers, i.e., retain the classifiers with high predictive accuracy and eliminate those
with a poor one according to a user's predefined threshold.
Random Prism's predictive accuracy
N
has been evaluated empirically on
several datasets of the UCI repository [
3
,
20
]; and it has been found that Random
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