Fuzzy Clustering and Genetic Algorithms - Biomedical Signal Analysis: Contemporary Methods and Applications - page 239

rate η 0 and the maximum number of iterations N . Set the iteration
counter equal to zero, ν = 0. Randomly generate an initial codebook
L =

{

L 1,0 ,

··· , L c,0 }

.
2. Adaptation, part I: Compute the updated learning rate η = η 0 1

N .

ν

−

Also set ν = ν +1.
3. Adaptation, part II: For each input vector x find the winning proto-
type based on the equation

2 < 2 ,

|| x − L i,ν−1 || || x − L j,ν−1 || ∀ j = i (7.86)

Determine the membership functions u ir,ν using

u ir,ν = u ||

,

L i,ν−1 || 2 x −

∀ r = i. (7.87)

|| x − L r,ν−1 || 2

Determine w ir,ν using

w ir,ν = u ||

,

L i,ν−1 || 2

x −

∀ r

= i.

(7.88)

|| x − L r,ν−1 || 2

Determine n ir,ν using

|| w ir,ν ,

2

x − L i,ν−1 ||

n ir,ν = u ir,ν − ∀ r = i. (7.89)

|| x − L r,ν−1 || 2

4. Adaptation part III: Determine the update of the winning prototype
L i using

c

L i,ν = L i,ν−1 + η ( x − L i,ν−1 )(1 + w ir,ν ) (7.90)

r=i

Determine the update of the nonwinning prototype L j = L i using

L j,ν = L j,ν−1 + η ( x

−

L j,ν−1 ) n ij,ν . (7.91)

5. Continuation: If ν = N , stop; else go to step 2.