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- W4379261292 abstract "Hierarchical clustering of networks consists in finding a tree of communities, such that lower levels of the hierarchy reveal finer-grained community structures. There are two main classes of algorithms tackling this problem. Divisive ($textit{top-down}$) algorithms recursively partition the nodes into two communities, until a stopping rule indicates that no further split is needed. In contrast, agglomerative ($textit{bottom-up}$) algorithms first identify the smallest community structure and then repeatedly merge the communities using a $textit{linkage}$ method. In this article, we establish theoretical guarantees for the recovery of the hierarchical tree and community structure of a Hierarchical Stochastic Block Model by a bottom-up algorithm. We also establish that this bottom-up algorithm attains the information-theoretic threshold for exact recovery at intermediate levels of the hierarchy. Notably, these recovery conditions are less restrictive compared to those existing for top-down algorithms. This shows that bottom-up algorithms extend the feasible region for achieving exact recovery at intermediate levels. Numerical experiments on both synthetic and real data sets confirm the superiority of bottom-up algorithms over top-down algorithms. We also observe that top-down algorithms can produce dendrograms with inversions. These findings contribute to a better understanding of hierarchical clustering techniques and their applications in network analysis." @default.
- W4379261292 created "2023-06-04" @default.
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- W4379261292 date "2023-06-01" @default.
- W4379261292 modified "2023-09-25" @default.
- W4379261292 title "When Does Bottom-up Beat Top-down in Hierarchical Community Detection?" @default.
- W4379261292 doi "https://doi.org/10.48550/arxiv.2306.00833" @default.
- W4379261292 hasPublicationYear "2023" @default.
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