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

Algorithm 3

PFCM.

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, 𝜂_𝑗: Degree of weight possibilistic,

and 𝜀: is the threshold representing the convergence error.

  Step  1.

(2)  (i) Initialize the matrix 𝑈 by random values in the interval [0,1].

  Step  2.

(4)   Repeat

   (i) Update the matrix 𝑉 cluster centers in (12).

(6)   (ii) Update the matrix 𝑈 degree of membership in (10).

  Until

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