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The dendrogram of DIANA can be constructed by letting the splinter group <math>C_\textrm{new}</math> be a child of the hollowed-out cluster <math>C_*</math> each time. This constructs a tree with <math>C_0</math> as its root and <math>n</math> unique single-object clusters as its leaves.
== Limitations ==
# '''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>.
# '''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>.
# '''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>.
# '''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=":3">{{Cite conference |last1=Herr |first1=Dominik |last2=Han |first2=Qi |last3=Lohmann |first3=Steffen |last4=Ertl |first4=Thomas |date=2016 |title=Visual Clutter Reduction through Hierarchy-based Projection of High-dimensional Labeled Data |url=https://graphicsinterface.org/wp-content/uploads/gi2016-14.pdf |conference=Graphics Interface |language=en-CA |doi=10.20380/gi2016.14 |access-date=2022-11-04 |website=Graphics Interface}}</ref>.
# '''Inability to Handle Non-Convex Shapes and Varying Densities''': Traditional hierarchical clustering methods, like many other clustering algorithms, often assume that clusters are convex and have similar densities. They may struggle to accurately identify clusters with non-convex shapes or varying densities <ref>{{Cite journal |last=Wani |first=Aasim Ayaz |date=2024-08-29 |title=Comprehensive analysis of clustering algorithms: exploring limitations and innovative solutions |journal=PeerJ Computer Science |language=en |volume=10 |pages=e2286 |doi=10.7717/peerj-cs.2286 |issn=2376-5992 |pmc=11419652 |pmid=39314716 |doi-access=free}}</ref>.
== Software ==
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