Fuzzy C-Means Clustering Algorithm

In the FCM algorithm, both the cluster center matrix C and membership matrix U undergo continuous updates through iterations until specific convergence criteria are met. This iterative optimization process involves calculating the distance between each data point and every cluster center while incorporating fuzzy membership weights. The algorithm employs a weighted least squares approach where membership values determine the influence of each data point on cluster center calculations. Key implementation aspects include: - Distance computation using Euclidean or other suitable metrics - Membership updating through exponentiated distance ratios - Cluster center recalculation as weighted averages of data points It's crucial to note that FCM exhibits high sensitivity to initial cluster center selection. Therefore, careful initialization strategies - such as random initialization with multiple restarts or using k-means++ initialization - are essential to avoid significant impact on final clustering results. The algorithm typically terminates when either membership changes fall below a threshold or maximum iterations are reached.