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PAC Learning with Bandit Feedback: Sharp Sample Complexity in the Realizable Setting Algorithms with Polynomially-Improved Approximation Factors for the $2 \rightarrow q$ Norm, and Applications A computational phase transition for learning-to-sample from Ising models Covering vertices by sequential stars Fermi-Dirac machines as quantizations of neurons A Comprehensive Evaluation of Vertex Elimination Algorithms for Algorithmic Differentiation A Tight Bound on Localization of Electrical Flows Optimal Dimension-Free Sampling for Regularized Classification Reducing the Randomness in Partition Oracles for Bounded Degree Minor-Free Graphs Beyond the Half-Approximation: Fair and Efficient Online Class Matching Efficient Uniform Sampling of Surjections via their Profiles Tractable Maximization of Budgeted Phylogenetic Diversity on Networks Utilizing Node Scanwidth Fairness in Aggregation: Optimal Top-$k$ and Improved Full Ranking Learning-Augmented Online Scheduling with Parsimonious Preemption Entropy Equivalence Testing Lumberjack: Better Differentially Private Random Forests through Heavy Hitter Detection in Trees The Secretary Problem with a Stochastic Precursor Polynomial-Time Robust Multiclass Linear Classification under Gaussian Marginals Efficient Banzhaf-Based Data Valuation for $k$-Nearest Neighbors Classification Block-Sphere Vector Quantization An Approximation Algorithm for Graph Label Selection Iterative Chow Filtering for Learning with Distribution Shift Complexity of Non-Log-Concave Sampling in Fisher Information Stochastic Matching via Local Sparsification Finite Sample Bounds for Learning with Score Matching What is Learnable in Valiant's Theory of the Learnable? Provable Quantization with Randomized Hadamard Transform Min-Max Optimization Requires Exponentially Many Queries Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm A proximal gradient algorithm for composite log-concave sampling
Chameleon2++: An Efficient and Scalable Variant Of Chamel...
Priyanshu Singh, Kapil Ahuja · 2025-01-06 · via cs.DS updates on arXiv.org

Hierarchical clustering remains a fundamental challenge in data mining, particularly when dealing with large-scale datasets where traditional approaches fail to scale effectively. Recent Chameleon-based algorithms - Chameleon2, M-Chameleon, and INNGS-Chameleon have proposed advanced strategies but they still suffer from $O(n^2)$ computational complexity, especially for large datasets. With Chameleon2 as the base algorithm, we introduce Chameleon2++ that addresses this challenge. Our algorithm has three parts. First, Graph Generation - we propose an approximate $k$-NN search instead of an exact one, specifically we integrate with the Annoy algorithm. This results in fast approximate nearest neighbor computation, significantly reducing the graph generation time. Second, Graph Partitioning - we propose use of a multi-level partitioning algorithm instead of a recursive bisection one. Specifically we adapt the hMETIS algorithm instead of the FM. This is because multi-level algorithms are robust to approximation introduced in the graph generation phase yielding higher-quality partitions, and that too with minimum configuration requirements. Third, Merging - we retain the flood fill heuristic that ensures connected balanced components in the partitions as well as efficient partition merging criteria leading to the final clusters. These enhancements reduce the overall time complexity to $O(n\log n)$, achieving scalability. On real-world benchmark datasets used in prior Chameleon works, Chameleon2++ delivers an average of 4% improvement in clustering quality. This demonstrates that algorithmic efficiency and clustering quality can co-exist in large-scale hierarchical clustering.