Kernel Fuzzy C-Means Clustering Algorithm Implementation

This implementation provides an efficient kernel-based Fuzzy C-Means (kernel-FCM) clustering algorithm designed for grouping similar data points based on distance and similarity metrics. The core algorithm extends traditional FCM by employing kernel functions to map input data into higher-dimensional feature spaces, enabling better separation of complex data structures. Key implementation features include: - Support for multiple kernel functions (RBF, polynomial, sigmoid) through modular kernel computation - Optimized cluster centroid updates using kernel-induced distance metrics - Efficient membership matrix calculation with convergence control parameters - Automated cluster validity index evaluation for optimal cluster number selection The code structure implements the kernel-FCM algorithm through three main components: 1. Kernel matrix precomputation using selected kernel function and parameters 2. Iterative membership update and centroid calculation in feature space 3. Convergence checking based on membership stability thresholds This implementation handles multidimensional data and provides visualization tools for cluster analysis results, making it particularly valuable for pattern recognition, image segmentation, and complex dataset analysis applications where linear separability assumptions don't hold.