## k-means++

 swMATH ID: 21622 Software Authors: D. Arthur, S. Vassilvitskii Description: 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. Homepage: https://dl.acm.org/citation.cfm?id=1283383.1283494 Related Software: UCI-ml; AS 136; PRMLT; clusfind; StreamKM++; Silhouettes; Scikit; PMTK; APCluster; apcluster; GitHub; t-SNE; J-MEANS; R; Adam; FLANN; clusterpath; BSDS; MNIST; TensorFlow Referenced in: 166 Publications

### Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
$$k$$-means++: the advantages of careful seeding. Zbl 1302.68273
Arthur, David; Vassilvitskii, Sergei
2007
all top 5

### Referenced by 439 Authors

 5 Jaiswal, Ragesh 3 Bhattacharya, Anup Kumar 3 Sra, Suvrit 2 Ailon, Nir 2 Aloise, Daniel 2 Bai, Ruibin 2 Blanchard, Gilles 2 Bonald, Thomas 2 Brunsch, Tobias 2 Chan, Laiwan 2 Chen, Zhitang 2 Deshpande, Amit 2 Dey, Tamal Krishna 2 Feldman, Dan 2 Giraud, Christophe 2 Gribonval, Rémi 2 Hämäläinen, Joonas 2 Hewitt, Mike 2 Hosseini, Reshad 2 Hu, Shoubo 2 Jiang, Xiaoping 2 Kärkkäinen, Tommi 2 Kaufmann, Emilie 2 Kendall, Graham 2 Keriven, Nicolas 2 Kim, Seoung Bum 2 Kumar, Amit 2 Lelarge, Marc 2 Mahajan, Meena 2 Mladenović, Nenad 2 Nimbhorkar, Prajakta 2 Pratap, Rameshwar 2 Röglin, Heiko 2 Rossi, Alfred 2 Schmidt, Melanie 2 Sidiropoulos, Anastasios 2 Sohler, Christian 2 Strohmer, Thomas 2 Traonmilin, Yann 2 Tremblay, Nicolas 2 Varadarajan, Kasturi R. 2 Verzelen, Nicolas 2 Xie, Ting 2 Yu, Jaehong 1 Ab Rahman, Khairul Shakir 1 Agarwal, Manu 1 Ahmadian, Sara 1 Aksoy, Selim 1 Alata, Olivier 1 Alencar, Alisson S. C. 1 Allen, Genevera I. 1 Alvo, Mayer 1 Amblard, Pierre-Olivier 1 An, Qiang 1 Arbel, Julyan 1 Arı, Çağlar 1 Arıkan, Orhan 1 Arthur, David 1 Asencio-Cortes, Gualberto 1 Avilés-Cruz, Carlos 1 Bach, Francis R. 1 Bagirov, Adil M. 1 Banerjee, Arindam 1 Barthelmé, Simon 1 Barwey, Shivam 1 Batet, Montserrat 1 Bazzi, Marya 1 Beckman, Paul G. 1 Benyó, Zoltán 1 Bera, Debajyoti 1 Bertsimas, Dimitris John 1 Beylkin, Gregory 1 Binétruy, Christophe 1 Bock, Stefan 1 Boubekki, Ahcène 1 Boutalbi, Rafika 1 Boyd, Nicholas 1 Brécheteau, Claire 1 Brefeld, Ulf 1 Brook, Bindi S. 1 Brunet-Saumard, Camille 1 Bunea, Florentina 1 Burgard, Jan Pablo 1 Canas, Guillermo D. 1 Capó, Marco 1 Castelo Damasceno, Nielsen 1 Cautis, Bogdan 1 Chandrashekar, Ashok 1 Chekuri, Chandra S. 1 Chen, Feiyu 1 Chen, Liyuan 1 Cheng, Yukun 1 Chiu, Angus 1 Choi, Seungjin 1 Coelho, André L. V. 1 Collet, Christophe 1 Correia, P. F. 1 Courbot, Jean-Baptiste 1 Crainic, Teodor Gabriel 1 Croucher, Mike ...and 339 more Authors
all top 5

### Referenced in 67 Serials

 10 Information Sciences 10 Machine Learning 8 Theoretical Computer Science 8 Journal of Machine Learning Research (JMLR) 7 Data Mining and Knowledge Discovery 6 Journal of Classification 6 Mathematical Problems in Engineering 4 Algorithmica 4 European Journal of Operational Research 4 Computational Statistics and Data Analysis 4 Statistics and Computing 3 Information Processing Letters 3 Computers & Operations Research 3 Neural Computation 3 Pattern Recognition 3 Mathematical Programming. Series A. Series B 3 Mathematical Statistics and Learning 2 The Annals of Statistics 2 SIAM Journal on Computing 2 Applied and Computational Harmonic Analysis 2 International Journal of Computer Vision 2 International Journal of Wavelets, Multiresolution and Information Processing 2 Advances in Data Analysis and Classification. ADAC 2 Electronic Journal of Statistics 2 Algorithms 1 Computer Methods in Applied Mechanics and Engineering 1 Journal of Computational Physics 1 Journal of Fluid Mechanics 1 ACM Transactions on Mathematical Software 1 Applied Mathematics and Computation 1 Calcolo 1 Fuzzy Sets and Systems 1 Journal of Multivariate Analysis 1 Journal of Optimization Theory and Applications 1 Computer Aided Geometric Design 1 Discrete & Computational Geometry 1 Journal of Scientific Computing 1 Signal Processing 1 Annals of Operations Research 1 Computational Geometry 1 Communications in Statistics. Simulation and Computation 1 SIAM Journal on Optimization 1 ETNA. Electronic Transactions on Numerical Analysis 1 Soft Computing 1 Journal of Combinatorial Optimization 1 Chaos 1 Combustion Theory and Modelling 1 Journal of High Energy Physics 1 Foundations of Computational Mathematics 1 Journal of Systems Science and Complexity 1 North American Actuarial Journal 1 Statistical Methods and Applications 1 Journal of Statistical Mechanics: Theory and Experiment 1 Mathematical Biosciences and Engineering 1 Oberwolfach Reports 1 Journal of Industrial and Management Optimization 1 Chebyshevskiĭ Sbornik 1 Computational & Mathematical Methods in Medicine 1 Statistical Analysis and Data Mining 1 The Annals of Applied Statistics 1 Journal of Computational and Graphical Statistics 1 Symmetry 1 Journal of Computational Geometry 1 Journal of Theoretical Biology 1 ISRN Biomathematics 1 SIAM/ASA Journal on Uncertainty Quantification 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
all top 5

### Referenced in 28 Fields

 100 Statistics (62-XX) 78 Computer science (68-XX) 31 Operations research, mathematical programming (90-XX) 9 Numerical analysis (65-XX) 8 Probability theory and stochastic processes (60-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Combinatorics (05-XX) 6 Biology and other natural sciences (92-XX) 4 Systems theory; control (93-XX) 4 Information and communication theory, circuits (94-XX) 2 General and overarching topics; collections (00-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Ordinary differential equations (34-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Functional analysis (46-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 General topology (54-XX) 2 Fluid mechanics (76-XX) 1 Algebraic geometry (14-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Partial differential equations (35-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Differential geometry (53-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Quantum theory (81-XX) 1 Relativity and gravitational theory (83-XX)