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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
Contraction Clustering (RASTER): A Very Fast Big Data Alg...
Gregor Ulm, Simon Smith, Adrian Nilsson, Emil Gustavsson, Mats J · 2019-07-08 · via cs.DS updates on arXiv.org

Clustering is an essential data mining tool for analyzing and grouping similar objects. In big data applications, however, many clustering algorithms are infeasible due to their high memory requirements and/or unfavorable runtime complexity. In contrast, Contraction Clustering (RASTER) is a single-pass algorithm for identifying density-based clusters with linear time complexity. Due to its favorable runtime and the fact that its memory requirements are constant, this algorithm is highly suitable for big data applications where the amount of data to be processed is huge. It consists of two steps: (1) a contraction step which projects objects onto tiles and (2) an agglomeration step which groups tiles into clusters. This algorithm is extremely fast in both sequential and parallel execution. Our quantitative evaluation shows that a sequential implementation of RASTER performs significantly better than various standard clustering algorithms. Furthermore, the parallel speedup is significant: on a contemporary workstation, an implementation in Rust processes a batch of 500 million points with 1 million clusters in less than 50 seconds on one core. With 8 cores, the algorithm is about four times faster.