Hierarchical, K-means, and EM Clustering Algorithms

This package implements three fundamental clustering algorithms: hierarchical, K-means, and EM clustering, each with distinct characteristics and practical applications. Hierarchical clustering builds a tree-like structure of nested clusters through either agglomerative (bottom-up) or divisive (top-down) approaches, typically implemented using linkage methods and dendrogram visualization for cluster similarity analysis. K-means clustering employs an iterative optimization process that partitions data into K clusters by minimizing within-cluster variance, commonly initialized with centroid selection methods like k-means++ and implementing convergence checks through maximum iteration limits or centroid stability thresholds - making it ideal for data mining and image segmentation tasks. The Expectation-Maximization (EM) algorithm provides a probabilistic framework based on Gaussian Mixture Models (GMM), where the E-step computes posterior probabilities of cluster assignments and the M-step updates model parameters through maximum likelihood estimation, particularly effective for handling overlapping clusters in mixed-data scenarios. These algorithms offer comprehensive coverage of clustering methodologies, enabling researchers and developers to better understand and analyze complex datasets through practical implementation details including initialization strategies, convergence criteria, and parameter tuning techniques.