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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''': Agglomerative: Agglomerative clustering, often referred to as a "bottom-up" approach, begins with each data point as an individual cluster. At each step, the algorithm merges the two most similar clusters based on a chosen distance metric (e.g., Euclidean distance) and linkage criterion (e.g., single-linkage, complete-linkage)
* '''Divisive''': Divisive clustering, known as a "top-down" approach, starts with all data points in a single cluster and recursively splits the cluster into smaller ones. At each step, the algorithm selects a cluster and divides it into two or more subsets, often using a criterion such as maximizing the distance between resulting clusters. Divisive methods are less common but can be useful when the goal is to identify large, distinct clusters first.
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== Limitations ==
Hierarchical clustering, particularly in its standard agglomerative form, presents several notable limitations: (a) Time Complexity: Hierarchical clustering, especially in its basic agglomerative form, has a high time complexity of O(n³). This becomes a significant bottleneck for large datasets, limiting its scalability <ref name="CLINK2">{{cite journal |author=D. Defays |year=1977 |title=An efficient algorithm for a complete-link method |journal=The Computer Journal |publisher=British Computer Society |volume=20 |issue=4 |pages=364–6 |doi=10.1093/comjnl/20.4.364 |doi-access=}}</ref>. (b) Scalability: Due to the time and space complexity, hierarchical clustering algorithms struggle to handle very large datasets efficiently <ref name=":2">{{Cite journal |last=Eppstein |first=David |date=2001-12-31 |title=Fast hierarchical clustering and other applications of dynamic closest pairs |url=https://dl.acm.org/doi/10.1145/351827.351829 |journal=ACM Journal of Experimental Algorithmics |volume=5 |pages=1–es |arxiv=cs/9912014 |doi=10.1145/351827.351829 |issn=1084-6654}}</ref>. (c) Sensitivity to Noise and Outliers: Hierarchical clustering methods can be sensitive to noise and outliers in the data, which can lead to the formation of inaccurate or misleading cluster hierarchies <ref name="SLINK2">{{cite journal |author=R. Sibson |year=1973 |title=SLINK: an optimally efficient algorithm for the single-link cluster method |url=http://www.cs.gsu.edu/~wkim/index_files/papers/sibson.pdf |journal=The Computer Journal |publisher=British Computer Society |volume=16 |issue=1 |pages=30–34 |doi=10.1093/comjnl/16.1.30 |doi-access=free}}</ref>. (d) Difficulty with High-Dimensional Data: In high-dimensional spaces, hierarchical clustering can face challenges due to the curse of dimensionality, where data points become sparse, and distance measures become less meaningful. This can result in poorly defined clusters<ref name=":6" />
== Software ==
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