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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