MATLAB Implementation of HCM and FCM Clustering Algorithms

HCM (Hard C-Means clustering) and FCM (Fuzzy C-Means clustering) are two classical clustering algorithms widely used in pattern recognition and data analysis fields. The MATLAB implementations of these algorithms, along with the fast algorithm for KFCM (Kernel Fuzzy C-Means clustering), provide excellent resources for graduation project students to understand the fundamental principles of clustering and their optimization methods. HCM represents a hard clustering approach where each data point strictly belongs to a single cluster, making it suitable for scenarios with clear data distributions. The MATLAB implementation typically involves initializing cluster centers, iteratively updating membership assignments, and recalculating centroids until convergence criteria are met. Key functions often include distance calculations using Euclidean metrics and centroid updates through mean computations. FCM employs fuzzy membership degrees, allowing data points to belong to multiple clusters with varying degrees of membership, making it more appropriate for situations with ambiguous cluster boundaries. The MATLAB implementation commonly features membership matrix initialization, iterative updates using exponentiated distance calculations, and centroid computations weighted by membership values. The algorithm typically converges when membership changes fall below a predefined threshold. KFCM enhances FCM by incorporating kernel functions that map data to higher-dimensional spaces, thereby improving the algorithm's ability to handle non-linearly separable data patterns. The fast algorithm optimizations primarily focus on computational efficiency, such as reducing iteration counts through improved convergence strategies or optimizing kernel matrix computations using dimensionality reduction techniques, making them more suitable for large-scale datasets. For graduation projects, these MATLAB implementations not only facilitate understanding of clustering fundamentals but also provide extensible code frameworks for further research. By integrating specific datasets with optimization strategies such as parameter tuning, initialization methods, or convergence acceleration techniques, students can enhance clustering performance and strengthen the innovative aspects of their theses. The code structure typically includes modular functions for data preprocessing, clustering core algorithms, validation metrics, and visualization components.