Fuzzy C-Means Clustering Method Implementation

In this implementation, we apply the Fuzzy C-Means clustering algorithm to classify data vectors. The algorithm partitions the dataset into three clusters and computes the corresponding cluster centers. The FCM method iteratively minimizes an objective function that measures the weighted distance between data points and cluster centers, using membership grades to indicate the degree of association for each data point with every cluster. Key implementation components include: - Initialization of cluster centers using random selection or k-means++ method - Calculation of membership matrix using distance metrics (typically Euclidean distance) - Update equations for cluster centers based on weighted averages of data points - Convergence criteria based on membership stability or maximum iterations The algorithm requires specification of the fuzzifier parameter (m) which controls the cluster fuzziness, typically set between 1.5 and 2.5. Common stopping conditions include maximum iteration count or minimal improvement in objective function value between iterations.