Enhanced 2D Data Clustering Using FCM and K-Means with Euclidean Distance Comparison

In this study, FCM and K-means clustering are in contrast to Fuzzy C Means (FCM), which initializes cluster centrist and calculates membership degrees for each data point, allowing for soft clustering with multiple degrees of membership to multiple clusters. Together, these methods update centroid and membership degrees until convergence. By contrast, K-means employs a hard clustering approach with a random centroid start according to the Euclidean distance; the closest centroids are allocated to each data point. The centroids were then updated interactively by applying an average the data points inside every cluster from start until the focus was reached. The comparative analysis highlights the FCM's flexibility and interoperability for datasets with natural overlap, while K-means is noted for its simple-to-understand implementation and efficiency with distinct clusters. This comparison of algorithms is based on dataset characteristics, with FCM excelling in complex, overlapping scenarios and K-means in clear, well-separated scenarios.