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

Algorithm 4

HPFCM.

Let 𝑋={𝑋_𝑖/𝑖={1⋯𝑁}} the data sets, 𝑀: the maximum number of iterations, 𝐾: the number of the clusters, 𝑈: the

matrix of membership degrees function, 𝑉: the matrix of cluster center, 𝑚: the fuzzy degree, Fuzzy_classification(): is the

function of fuzzy classification, F_obj(): the objective function, Possibilist_classification(): the possibilistic classification

function, 𝜂_𝑗: Degree of weight possibilistic, and 𝜖: the threshold Representing the convergence error.

(1) Step 1. Initialize the parameters

(2)  (i) 𝑚=1.5

(3)  (ii) Initialize the matrix 𝑉 by center clusters

(4)  (iii) Initialize the matrix 𝑈 by membership degrees, random values in the interval [0,1]

and it also satisfies the condition in (3).

(5) Step 2. Fuzzy process

(6) Repeat

(7)  𝑉^old=𝑉;𝑈^old=𝑈

(8)  Compute: [𝑈,𝑉]= Fuzzy_classification (𝑋,𝑈,𝑉,𝑚) // with (4) and (5)

(9)  𝑉^new=𝑉;𝑈^new=𝑈

(10) Until 𝑉^new−𝑉^old≤𝜀

(11) Step 3. Possibilist process

(12)  𝑊=𝑈^new // Initialize the matrix 𝑊 by 𝑈^new

(13)  𝑌=𝑉^new // Initialize the matrix 𝑌 by 𝑉^new

(14) Repeat

(15)  𝑌^old=𝑌;𝑊^old=𝑊

(16)  Compute: [𝑊,𝑌]=  Possibilist_classification (𝑋,𝑊,𝑌,𝜂) // with (7) and (8)

(17)  𝑌^new=𝑌;𝑊^new=𝑊

(18) Until 𝑌^new−𝑌^old≤𝜀