Algorithm 1. Hierarchical Fuzzy C-Means Clustering

Input: Initialize list of data $X=\left\{X_1,\cdots ,X_n\right\}$ with size n, threshold t, number of cluster c

Output: List of c cluster centers $C=\left\{C_1,\cdots ,C_c\right\}$

1. for c = 1 to n

2. List candidateList = $\arg {\min }_c{\displaystyle {\sum }_{i=1}^n{\displaystyle {\sum }_{j=1}^c{w}_{ij}^m{\Vert x_i-c_j\Vert }^2}}$

3. Apply Silhouette Width on candidateList, give value q

4. end for

5. Choose optimal q, List finallist = candidateList

6. for each cluster set s in finallist

7. int clusterSize = s.size()

8. if(clusterSize > t)

9. n = c

10. do 1-18

11. end if

12. else if All clusterSize <= t

13. return C

14. end else if

15. else if All clusterSize doesn’t change

16. return C

17. end else if

18. end for