k-means++: The advantages of careful seeding. The k-means method is a widely used clustering technique that seeks to minimize the average squared distance between points in the same cluster. Although it offers no accuracy guarantees, its simplicity and speed are very appealing in practice. By augmenting k-means with a very simple, randomized seeding technique, we obtain an algorithm that is Θ(logk)-competitive with the optimal clustering. Preliminary experiments show that our augmentation improves both the speed and the accuracy of k-means, often quite dramatically.

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  1. Deshpande, Amit; Pratap, Rameshwar: Sampling-based dimension reduction for subspace approximation with outliers (2021)
  2. Zhang, Dongmei; Cheng, Yukun; Li, Min; Wang, Yishui; Xu, Dachuan: Approximation algorithms for spherical (k)-means problem using local search scheme (2021)
  3. Ahmadian, Sara; Norouzi-Fard, Ashkan; Svensson, Ola; Ward, Justin: Better guarantees for (k)-means and Euclidean (k)-median by primal-dual algorithms (2020)
  4. Bunea, Florentina; Giraud, Christophe; Luo, Xi; Royer, Martin; Verzelen, Nicolas: Model assisted variable clustering: minimax-optimal recovery and algorithms (2020)
  5. Capó, Marco; Pérez, Aritz; Lozano, Jose A.: An efficient (K)-means clustering algorithm for tall data (2020)
  6. Ding, Hu; Xu, Jinhui: A unified framework for clustering constrained data without locality property (2020)
  7. Duan, Leo L.: Latent simplex position model: high dimensional multi-view clustering with uncertainty quantification (2020)
  8. Feldman, Dan; Schmidt, Melanie; Sohler, Christian: Turning big data into tiny data: constant-size coresets for (k)-means, PCA, and projective clustering (2020)
  9. Feng, Ben Mingbin; Tan, Zhenni; Zheng, Jiayi: Efficient simulation designs for valuation of large variable annuity portfolios (2020)
  10. Guillaume, Serge; Ros, Frédéric: A family of unsupervised sampling algorithms (2020)
  11. Hämäläinen, Joonas; Alencar, Alisson S. C.; Kärkkäinen, Tommi; Mattos, César L. C.; Souza Júnior, Amauri H.; Gomes, João P. P.: Minimal learning machine: theoretical results and clustering-based reference point selection (2020)
  12. Hosseini, Reshad; Sra, Suvrit: An alternative to EM for Gaussian mixture models: batch and stochastic Riemannian optimization (2020)
  13. Irmatov, Anvar Adkhamovich; Irmatova, Èl’nura Anvarovna: Estimation of the inclusive development index based on the REL-PCANet neural network model (2020)
  14. Irons, Linda; Huang, Huang; Owen, Markus R.; O’Dea, Reuben D.; Meininger, Gerald A.; Brook, Bindi S.: Switching behaviour in vascular smooth muscle cell-matrix adhesion during oscillatory loading (2020)
  15. Krassovitskiy, Alexander; Mladenovic, Nenad; Mussabayev, Rustam: Decomposition/aggregation (k)-means for big data (2020)
  16. Ling, Shuyang; Strohmer, Thomas: Certifying global optimality of graph cuts via semidefinite relaxation: a performance guarantee for spectral clustering (2020)
  17. Lü, Hongliang; Arbel, Julyan; Forbes, Florence: Bayesian nonparametric priors for hidden Markov random fields (2020)
  18. Otsuka, Hajime; Takemoto, Kenta: Deep learning and k-means clustering in heterotic string vacua with line bundles (2020)
  19. Rezaei, Mohammad: Improving a centroid-based clustering by using suitable centroids from another clustering (2020)
  20. Sayed, Gehad Ismail; Darwish, Ashraf; Hassanien, Aboul Ella: Binary whale optimization algorithm and binary moth flame optimization with clustering algorithms for clinical breast cancer diagnoses (2020)

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