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Hierarchical Clustering
In data mining and statistics, hierarchical clustering (also called hierarchical cluster analysis or HCA) is a method of cluster analysis that seeks to build a hierarchy of clusters. Strategies for hierarchical clustering generally fall into two categories: - Agglomerative: This is a "bottom-up" approach: Each observation starts in its own cluster, and pairs of clusters are merged as one moves up the hierarchy.
The standard algorithm for hierarchical agglomerative clustering(HAC) has a time complexity of O(n3){\displaystyle {\mathcal {O}}(n^{3})} and requires Ω(n2){\displaystyle \Omega (n^{2})} memory, which makes it too slow for even medium data sets. ALGLIB implements several hierarchical clustering algorithms (single-link, complete-link, Ward) in C++ and C# with O(n²) memory and O(n³) run time. PMID 15585525.^ Basalto, Nicolas; Bellotti, Roberto; De Carlo, Francesco; Facchi, Paolo; Pantaleo, Ester; Pascazio, Saverio (2007-06-15).
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