Unsupervised Approach Data Analysis Based on Fuzzy Possibilistic Clustering: Application to Medical Image MRI

Algorithm 1

FCM.

Let 𝑋={𝑋_𝑖/𝑖={1⋯𝑁}} the data sets, 𝐾: the number of cluster, 𝑈 = (𝑢_𝑖𝑗)_{1≤𝑖≤𝑁,1≤𝑗≤𝐾} is the matrix of membership degrees

function, 𝑉=(𝑣_𝑖𝑗)_{1≤𝑖≤𝑁,1≤𝑗≤𝐾} is the matrix of cluster centers, 𝑚: the degree of fuzzy, and 𝜀: is the threshold representing

convergence error.

(1) Step 1.

(2)  (i) Initialize the matrix 𝑈 by random values in the interval [0,1] and it also satisfies the condition in (3).

(3) Step 2.

(4)   Repeat

(5)  (i) Update the matrix 𝑉 cluster centers in (5).

(6)  (ii) Update the matrix 𝑈 degree of membership in (4).

(7)   Until

(8)    Stability of the matrix 𝑉,  𝑉^new−𝑉^old≤𝜀