An Application of a Hybrid Intelligent System for Diagnosing Primary Headaches

. 2021 Feb 16;18(4):1890. doi: 10.3390/ijerph18041890

Algorithm 1: Weighted fuzzy c-means clustering algorithm

Begin
Step 1:
---Initialization.
X, c, ε > 0, W
Step 2:
---Randomly select V cluster centers.
2 ≤ c ≤ N
Step 3:
---Choose an appropriate level of cluster fuzzinessf.
f [1, ∞], f > 1
Step 4:
---Choose an appropriate membership matrix U with size N × c × M
U_ijm ∈ [0, 1] and

\sum_{j = 1}^{c} U_{i j m} = 1

for a fixed value of m
Step 5:
---Calculate the cluster centers.
Repeat for jth cluster and its mth dimension

C C_{j m} = \frac{\sum_{i = 1}^{N} U_{i j m}^{f} x_{i m} w_{m}}{\sum_{i + 1}^{N} U_{i j m}^{f}}

Step 6:
---Calculate the Euclidean distance

D_{i j m} = ‖ (x_{i m} w_{m} - C C_{j m}) ‖

Step 7:
---Update fuzzy membership matrix U according to D_ijm

U_{i j m} = \frac{1}{\sum_{c = 1}^{C} {(\frac{D_{i j m}}{D_{i c m}})}^{\frac{2}{f - 1}}}

Step 8:
Until U ≤ ε

End.