Information Technology Reference
In-Depth Information
Reset R
k
i
. R
k
i
represents
the i
th
RecBF of class k, and
W
k
i
represents its weight.
∀
R
k
i
{
W
k
i
= 0
(a,b,c,d)
k
i
= (a,-,-,d)
k
i
}
∀
pattern (x,µ) {
k = argmax
1•kc
{µ
k
(x)}
if
∃
R
k
i
:x
∈
[a
k
i
,d
k
i
] then
W
k
i
= W
k
i
+ 1
covered()
else
m
k
= m
k
+ 1; a
k
mk
= 1
(a,b,c,d)
k
mk
= (-,x,x,-)
end if
∀
R
i
j
with
i
(x) = 0 {
if x
∈
[a
i
i
,d
k
i
] then
shrink()
end if
}
}
covered()
stretch the core-
region of R
k
i
selected to
(x,μ).
commit
: a new RecBF is
created, having its core-
region=pattern.
If a pattern is incorrectly
covered by a RecBF of an-
other class, its support-
region will be reduced until
the conflict will be solved.
This action is done in
shrink()
.
Fig. 2.3.
One epoch of the DDA/RecBF algorithm. The algorithm iterates until stability of the
RecBFs is reached.
(2)
Support
Region
(1)
Core Region
(3)
(4)
Fig. 2.4.
An example of the execution of the DDA/RecBF algorithm for a 2-dimensional sys-
tem. (1) shows 3 patterns from one class determining a RecBF, (2) shows 2 patterns from an-
other class and how they cause the creation of a new RecBF and shrink the existing one, (3) and
(4) show the different RecBFs created when the inclusion of new pattern is done, just varying
the x coordinate: outside and inside the core-region of the other class. The x and y axis show
the different membership functions created.
However, in our case we work with imbalanced or highly imbalanced datasets, and
to avoid granulation of the membership functions of the minor-class, it is absolutely
necessary to generalize this class, because the main problem is when the method has
to classify/test patterns belonging to this class, not shown during the training process.
