Theory of Agglomerative Hierarchical Clustering

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Agglomerative hierarchical clustering is explored through recent theoretical advancements, challenging the notion that its foundational theory is complete. The book presents a general algorithm for standard linkage methods, utilizing a recursive subprogram to illustrate dendrogram outputs. It proves a fundamental theorem for single linkage with fuzzy graphs and discusses theoretical properties like dendrogram reversals. Additionally, it examines new methods involving positive-definite kernels and their implications for the Ward method, making the findings relevant for both theoretical exploration and practical applications.