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A cost function for similarity-based hierarchical clustering

arXiv 1510.05043 ↗First posted 16 Oct 2015cs.DS cs.LG stat.MLcited by 63

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Abstract (arXiv)

The development of algorithms for hierarchical clustering has been hampered by a shortage of precise objective functions. To help address this situation, we introduce a simple cost function on hierarchies over a set of points, given pairwise similarities between those points. We show that this criterion behaves sensibly in canonical instances and that it admits a top-down construction procedure with a provably good approximation ratio.

Key facts. Cited by 63 papers in the map (data through 7 Oct 2026). First posted on arXiv 16 Oct 2015.

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Citing papers per year: 2021: 14; 2022: 11; 2023: 11; 2024: 12; 2025: 2; 2026: 13.

63 papers.

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  1. 2021Hyperbolic Deep Neural Networks: A Surveycited by 138
  2. 2023Hyperbolic Deep Learning in Computer Vision: A Surveycited by 72
  3. 2021Provably efficient, succinct, and precise explanationscited by 32
  4. 2022HIER: Metric Learning Beyond Class Labels via Hierarchical Regularizationcited by 26
  5. 2022Contrastive Multi-view Hyperbolic Hierarchical Clusteringcited by 19
  6. 2023Hyperbolic Diffusion Embedding and Distance for Hierarchical Representation Learningcited by 18
  7. 2021Neural Distance Embeddings for Biological Sequencescited by 17
  8. 2021Supervised Tree-Wasserstein Distancecited by 10
  9. 2023GeoPhy: Differentiable Phylogenetic Inference via Geometric Gradients of Tree Topologiescited by 9
  10. 2021Hierarchical Agglomerative Graph Clustering in Nearly-Linear Timecited by 8
  11. 2021Hierarchical Clustering: O(1)-Approximation for Well-Clustered Graphscited by 8
  12. 2023Nearly-Optimal Hierarchical Clustering for Well-Clustered Graphscited by 7
38 more
  1. 2021Randomized Dimensionality Reduction for Facility Location and Single-Linkage Clusteringcited by 6
  2. 2021An Information-theoretic Perspective of Hierarchical Clusteringcited by 6
  3. 2021Fairness Degrading Adversarial Attacks Against Clustering Algorithmscited by 5
  4. 2023Differentially-Private Hierarchical Clustering with Provable Approximation Guaranteescited by 5
  5. 2024Tree-Wasserstein Distance for High Dimensional Data with a Latent Feature Hierarchycited by 5
  6. 2022Generalized Reductions: Making any Hierarchical Clustering Fair and Balanced with Low Costcited by 4
  7. 2023Hyperbolic Geometry in Computer Vision: A Surveycited by 4
  8. 2022HyperAid: Denoising in hyperbolic spaces for tree-fitting and hierarchical clusteringcited by 3
  9. 2024An Axiomatic Definition of Hierarchical Clusteringcited by 3
  10. 2024From Logits to Hierarchies: Hierarchical Clustering made Simplecited by 3
  11. 2022Sublinear Algorithms for Hierarchical Clusteringcited by 2
  12. 2023CEO: Corpus-based Open-Domain Event Ontology Inductioncited by 2
  13. 2023Hierarchical clustering with dot products recovers hidden tree structurecited by 2
  14. 2023Fair Polylog-Approximate Low-Cost Hierarchical Clusteringcited by 2
  15. 2024Optimization of Inter-group Criteria for Clustering with Minimum Size Constraintscited by 2
  16. 2024A Near-Linear Time Approximation Algorithm for Beyond-Worst-Case Graph Clusteringcited by 2
  17. 2024On the cohesion and separability of average-link for hierarchical agglomerative clusteringcited by 2
  18. 2021Exact and Approximate Hierarchical Clustering Using A*cited by 1
  19. 2021ParChain: A Framework for Parallel Hierarchical Agglomerative Clustering using Nearest-Neighbor Chaincited by 1
  20. 2021Hierarchical Clustering: New Bounds and Objectivecited by 1
  21. 2022Faster One-Sample Stochastic Conditional Gradient Method for Composite Convex Minimizationcited by 1
  22. 2022Tangles and Hierarchical Clusteringcited by 1
  23. 2022Stars: Tera-Scale Graph Building for Clustering and Graph Learningcited by 1
  24. 2023When Does Bottom-up Beat Top-down in Hierarchical Community Detection?cited by 1
  25. 2024A Novel Approach to Regularising 1NN classifier for Improved Generalizationcited by 1
  26. 2024Fair Clustering: Critique, Caveats, and Future Directionscited by 1
  27. 2024Breaking Information Cocoons: A Hyperbolic Framework for Balancing Exploration and Exploitation in Recommender Systemscited by 1
  28. 2026Do Sparse Autoencoders Learn Meaningful Concept Hierarchies?cited by 1
  29. 2021Distribution free optimality intervals for clusteringcited by 0
  30. 2021An objective function for order preserving hierarchical clusteringcited by 0
  31. 2022Expanding the class of global objective functions for dissimilarity-based hierarchical clusteringcited by 0
  32. 2022Monitoring the Dynamic Networks of Stock Returnscited by 0
  33. 2022A Revenue Function for Comparison-Based Hierarchical Clusteringcited by 0
  34. 2023Constrained Hierarchical Clustering via Graph Coarsening and Optimal Cutscited by 0
  35. 2024Untangling Gaussian Mixturescited by 0
  36. 2024PE: A Poincare Explanation Method for Fast Text Hierarchy Generationcited by 0
  37. 2024Multi-View Stochastic Block Modelscited by 0
  38. 2025On the Price of Differential Privacy for Hierarchical Clusteringcited by 0

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