Image Processing Reference
In-Depth Information
Algorithm: Fuzzy-Crisp Difference RECA Approximations
foreach Data object x
i
do
Determine the closest cluster center center(C
i
) for x
i
Increment Lower(C
i
) by fuzzy membership value of x
i
Increment Upper(C
i
) by fuzzy membership value of x
i
foreach Cluster C
k
not further then eps from D do
Increment Upper(C
k
) by fuzzy membership value of x
i
end
for l = 1 to number of data clusters do
roughness(l) = 1 - [ Lower(l) / Upper(l)]
Fuzzy Rough entropy = 0
for l = 1 to number of data clusters do
Fuzzy Rough entropy = Fuzzy Rough entropy−
e
2
·roughness(l)·
log(roughness(l))
|d(x
i
, C
m
)−d
min
dist
|≤
dist
In Fuzzy-Fuzzy threshold RECA, the membership values of the analyzed data point to
all the clusters centers are computed. Next, the data point is assigned to the lower and
upper approximation of the closest cluster and its fuzzy membership value to this cluster
center center(C) is remembered. Additionally, if the fuzzy membership value to other
cluster center or centers is greater than predefined fuzzy threshold
f uzzy
- this data object
is assigned to this cluster upper approximation or approximations. For each data point
x
i
, the approximations are increased by this data point membership value µ
C
m
(x
i
) to the
clusters C
m
that satisfy the condition:
µ
C
m
(x
i
)≥
f uzz
In Fuzzy-Fuzzy RECA setting, the membership values of the analyzed object to all the clus-
ters centers are computed. Afterwards data object assignment is performed to lower and
upper approximation of the closest cluster with the distance to the closest cluster C
l
remem-
bered as d
min
f uzz
= d(x
i
, C
l
, ) Additionally, if difference between the fuzzy distance to other
clusters and the fuzzy distance to the closest cluster d
min
f uzz
= d(x
i
, C
l
) is less than predefined
distance threshold
f uzz
- this data object is assigned to this cluster approximations. Lower
and upper approximation calculation follows steps presented in Algorithm 5. For each data
point x
i
, the approximations are increased by this data point fuzzy membership value of
the clusters C
m
that satisfy the condition:
(µ
C
m
(x
i
)−d
min
f uzz
)≤
f uzz
Approximations are increased by fuzzy membership value of the given data object to the
cluster center.
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