references.bib

@article{kmeans,
    author  = "S. Lloyd",
    title   = "{L}east {S}quares {Q}uantization in {PCM}",
    journal = "IEEE Transactions on Information Theory",
    year    = {1982}
}

@article{ostro,
    author  = "R. Ostrovsky, Y. Rabani, L. Schulman and C. Swamy",
    title   = "The {E}ffectiveness of {L}loyd-type {M}ethods for the {K}-{M}eans {P}roblem",
    journal = "Symposium on Foundations of Computer Science",
    year    = {2006}
}

@inproceedings{kmeanspp,
    author    = {Arthur, David and Vassilvitskii, Sergei},
    title     = {K-Means++: The {A}dvantages of {C}areful {S}eeding},
    year      = {2007},
    isbn      = {9780898716245},
    publisher = {Society for Industrial and Applied Mathematics},
    address   = {USA},
    booktitle = {Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms},
    pages     = {1027–1035},
    numpages  = {9},
    location  = {New Orleans, Louisiana},
    series    = {SODA ’07}
}

@article{marton1,
    author  = "Marton, K",
    title   = "A {M}easure {C}oncentration {I}nequality for {C}ontracting {M}arkov {C}hains",
    journal = "Geometric and Functional Analysis",
    year    = "1996"
}

@article{marton2,
    author  = "Marton, K",
    title   = "K. {M}easure {C}oncentration for a {C}lass of {R}andom {P}rocesses",
    journal = "Probability Theory and Related Fields",
    year    = "1998"
}

@article{samson,
    author  = "Samson, Paul-Marie",
    title   = "Concentration of {M}easure {I}nequalities for {M}arkov {C}hains and $\Phi$-{M}ixing {P}rocesses",
    journal = "The Annals of Probability",
    year    = "2000"
}

@article{kontor,
    author  = "Kontorovich, Leonid and Ramanan, Kavita",
    title   = "Concentration {I}nequalities for {D}ependent {R}andom {V}ariables via the {M}artingale {M}ethod",
    journal = "The Annals of Probability",
    year    = "2008"
}

@inproceedings{parallel-kmeans,
    author    = "Zhao, Weizhong and Ma, Huifang and He, Qing",
    editor    = "Jaatun, Martin Gilje and Zhao, Gansen and Rong, Chunming",
    title     = "Parallel K-Means Clustering Based on MapReduce",
    booktitle = "Cloud Computing",
    year      = "2009",
    publisher = "Springer Berlin Heidelberg",
    address   = "Berlin, Heidelberg",
    pages     = "674--679",
    isbn      = "978-3-642-10665-1"
}

@article{scalable-kmeanspp,
    author     = {Bahmani, Bahman and Moseley, Benjamin and Vattani, Andrea and Kumar, Ravi and Vassilvitskii, Sergei},
    title      = {Scalable K-Means++},
    year       = {2012},
    issue_date = {March 2012},
    publisher  = {VLDB Endowment},
    volume     = {5},
    number     = {7},
    issn       = {2150-8097},
    url        = {https://doi.org/10.14778/2180912.2180915},
    doi        = {10.14778/2180912.2180915},
    journal    = {Proc. VLDB Endow.},
    month      = mar,
    pages      = {622–633},
    numpages   = {12}
}

@inproceedings{approx-kmeanspp,
    title     = {Approximate K-Means++ in Sublinear Time},
    author    = {Olivier Bachem and Mario Lucic and S. Hamed Hassani and Andreas Krause},
    booktitle = {AAAI},
    year      = {2016}
}

@article{paulin,
    author    = "Paulin, Daniel",
    doi       = "10.1214/EJP.v20-4039",
    fjournal  = "Electronic Journal of Probability",
    journal   = "Electron. J. Probab.",
    pages     = "32 pp.",
    pno       = "79",
    publisher = "The Institute of Mathematical Statistics and the Bernoulli Society",
    title     = "Concentration inequalities for Markov chains by Marton couplings and spectral methods",
    url       = "https://doi.org/10.1214/EJP.v20-4039",
    volume    = "20",
    year      = "2015"
}

@article{forgy,
    author    = "Forgy, E. W.",
    title     = "Cluster analysis of multivariate data : efficiency versus interpretability of classifications",
    journal   = "Biometrics",
    ISSN      = "",
    publisher = "",
    year      = "1965",
    month     = "",
    volume    = "21",
    number    = "",
    pages     = "768-769",
    URL       = "https://ci.nii.ac.jp/naid/10009668881/en/",
    DOI       = "",
}

@article{maxmin,
    title    = "Clustering to minimize the maximum intercluster distance",
    journal  = "Theoretical Computer Science",
    volume   = "38",
    pages    = "293 - 306",
    year     = "1985",
    issn     = "0304-3975",
    doi      = "https://doi.org/10.1016/0304-3975(85)90224-5",
    url      = "http://www.sciencedirect.com/science/article/pii/0304397585902245",
    author   = "Teofilo F. Gonzalez",
    keywords = "Algorithms, clustering, NP-completeness, approximation algorithms, minimizing the maximum intercluster distance",
    abstract = "The problem of clustering a set of points so as to minimize the maximum intercluster distance is studied. An O(kn) approximation algorithm, where n is the number of points and k is the number of clusters, that guarantees solutions with an objective function value within two times the optimal solution value is presented. This approximation algorithm succeeds as long as the set of points satisfies the triangular inequality. We also show that our approximation algorithm is best possible, with respect to the approximation bound, if P ≠ NP."
}

@book{ka,
    author    = {Kaufman, Leonard and Rousseeuw, Peter},
    year      = {2009},
    month     = {09},
    pages     = {},
    publisher = {O'Reilly},
    title     = {Finding Groups in Data: An Introduction to Cluster Analysis},
    isbn      = {9780470317488}
}

@article{pena,
    title    = "An empirical comparison of four initialization methods for the K-Means algorithm",
    journal  = "Pattern Recognition Letters",
    volume   = "20",
    number   = "10",
    pages    = "1027 - 1040",
    year     = "1999",
    issn     = "0167-8655",
    doi      = "https://doi.org/10.1016/S0167-8655(99)00069-0",
    url      = "http://www.sciencedirect.com/science/article/pii/S0167865599000690",
    author   = "J.M Peña and J.A Lozano and P Larrañaga",
    keywords = "-Means algorithm, -Means initialization, Partitional clustering, Genetic algorithms",
    abstract = "In this paper, we aim to compare empirically four initialization methods for the K-Means algorithm: random, Forgy, MacQueen and Kaufman. Although this algorithm is known for its robustness, it is widely reported in the literature that its performance depends upon two key points: initial clustering and instance order. We conduct a series of experiments to draw up (in terms of mean, maximum, minimum and standard deviation) the probability distribution of the square-error values of the final clusters returned by the K-Means algorithm independently on any initial clustering and on any instance order when each of the four initialization methods is used. The results of our experiments illustrate that the random and the Kaufman initialization methods outperform the rest of the compared methods as they make the K-Means more effective and more independent on initial clustering and on instance order. In addition, we compare the convergence speed of the K-Means algorithm when using each of the four initialization methods. Our results suggest that the Kaufman initialization method induces to the K-Means algorithm a more desirable behaviour with respect to the convergence speed than the random initialization method."
}


@article{celebi,
    title    = "A comparative study of efficient initialization methods for the k-means clustering algorithm",
    journal  = "Expert Systems with Applications",
    volume   = "40",
    number   = "1",
    pages    = "200 - 210",
    year     = "2013",
    issn     = "0957-4174",
    doi      = "https://doi.org/10.1016/j.eswa.2012.07.021",
    url      = "http://www.sciencedirect.com/science/article/pii/S0957417412008767",
    author   = "M. Emre Celebi and Hassan A. Kingravi and Patricio A. Vela",
    keywords = "Partitional clustering, Sum of squared error criterion, k-means, Cluster center initialization",
    abstract = "K-means is undoubtedly the most widely used partitional clustering algorithm. Unfortunately, due to its gradient descent nature, this algorithm is highly sensitive to the initial placement of the cluster centers. Numerous initialization methods have been proposed to address this problem. In this paper, we first present an overview of these methods with an emphasis on their computational efficiency. We then compare eight commonly used linear time complexity initialization methods on a large and diverse collection of data sets using various performance criteria. Finally, we analyze the experimental results using non-parametric statistical tests and provide recommendations for practitioners. We demonstrate that popular initialization methods often perform poorly and that there are in fact strong alternatives to these methods."
}

@inproceedings{helan,
    author    = { {Ji He} and {Man Lan} and {Chew-Lim Tan} and {Sam-Yuan Sung} and {Hwee-Boon Low}},
    booktitle = {2004 IEEE International Joint Conference on Neural Networks (IEEE Cat. No.04CH37541)},
    title     = {Initialization of cluster refinement algorithms: a review and comparative study},
    year      = {2004},
    volume    = {1},
    number    = {},
    pages     = {297-302}
}

@article{douglas,
    author  = {Steinley, Douglas and Brusco, Michael},
    year    = {2007},
    month   = {02},
    pages   = {99-121},
    title   = {Initializing K-means Batch Clustering: A Critical Evaluation of Several Techniques},
    volume  = {24},
    journal = {Journal of Classification},
    doi     = {10.1007/s00357-007-0003-0}
}

@article{sami,
    author  = {Sieranoja, Sami},
    year    = {2019},
    month   = {04},
    pages   = {},
    title   = {How much k-means can be improved by using better initialization and repeats?},
    volume  = {93},
    journal = {Pattern Recognition},
    doi     = {10.1016/j.patcog.2019.04.014}
}

@inproceedings{dist-kmeanspp,
    author    = {Bachem, Olivier and Lucic, Mario and Krause, Andreas},
    title     = {Distributed and Provably Good Seedings for K-Means in Constant Rounds},
    year      = {2017},
    publisher = {JMLR.org},
    booktitle = {Proceedings of the 34th International Conference on Machine Learning - Volume 70},
    pages     = {292–300},
    numpages  = {9},
    location  = {Sydney, NSW, Australia},
    series    = {ICML’17}
}

@incollection{fast-kmeanspp,
    title     = {Fast and Provably Good Seedings for k-Means},
    author    = {Bachem, Olivier and Lucic, Mario and Hassani, Hamed and Krause, Andreas},
    booktitle = {Advances in Neural Information Processing Systems 29},
    editor    = {D. D. Lee and M. Sugiyama and U. V. Luxburg and I. Guyon and R. Garnett},
    pages     = {55--63},
    year      = {2016},
    publisher = {Curran Associates, Inc.},
    url       = {http://papers.nips.cc/paper/6478-fast-and-provably-good-seedings-for-k-means.pdf}
}

@incollection{stream-kmeanspp,
    title     = {Streaming k-means approximation},
    author    = {Nir Ailon and Ragesh Jaiswal and Claire Monteleoni},
    booktitle = {Advances in Neural Information Processing Systems 22},
    editor    = {Y. Bengio and D. Schuurmans and J. D. Lafferty and C. K. I. Williams and A. Culotta},
    pages     = {10--18},
    year      = {2009},
    publisher = {Curran Associates, Inc.},
    url       = {http://papers.nips.cc/paper/3812-streaming-k-means-approximation.pdf}
}

@inproceedings{adaptive-kmeanspp,
    author    = {Aggarwal, Ankit and Deshpande, Amit and Kannan, Ravindran},
    year      = {2009},
    month     = {01},
    pages     = {15-28},
    title     = {Adaptive Sampling for k-Means Clustering},
    booktitle = {APPROX-RANDOM},
    doi       = {10.1007/978-3-642-03685-9_2}
}

@article{telgarsky2013moment,
    author    = {Matus Telgarsky and Sanjoy Dasgupta},
    title     = {Moment-based Uniform Deviation Bounds for {\textdollar}k{\textdollar}-means and Friends},
    journal   = {CoRR},
    volume    = {abs/1311.1903},
    year      = {2013},
    url       = {http://arxiv.org/abs/1311.1903},
    archivePrefix = {arXiv},
    eprint    = {1311.1903},
    timestamp = {Mon, 13 Aug 2018 16:47:08 +0200},
    biburl    = {https://dblp.org/rec/journals/corr/TelgarskyD13.bib},
    bibsource = {dblp computer science bibliography, https://dblp.org}
}