Clustering: Hierarchical and K-means Methods

This lecture covers clustering algorithms aiming to optimize homogeneity and separability criteria, including hierarchical clustering, centroid-based clustering, and density-based clustering. It explains the construction methods of hierarchical clustering, such as agglomerative and divisive approaches, focusing on agglomerative clustering. The lecture also discusses linkage functions like single, complete, average, and centroid linkage to ensure cluster separability. It explores Ward's clustering method for homogeneity and the k-means method as an alternative to exploring all possible partitions. The lecture details the Lloyd algorithm for k-means, discussing convergence, computational cost, and cluster formation. It also introduces the k-means++ algorithm to mitigate suboptimal solutions due to random initialization.