IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0041713.html
   My bibliography  Save this article

A Multicriteria Decision Making Approach for Estimating the Number of Clusters in a Data Set

Author

Listed:
  • Yi Peng
  • Yong Zhang
  • Gang Kou
  • Yong Shi

Abstract

Determining the number of clusters in a data set is an essential yet difficult step in cluster analysis. Since this task involves more than one criterion, it can be modeled as a multiple criteria decision making (MCDM) problem. This paper proposes a multiple criteria decision making (MCDM)-based approach to estimate the number of clusters for a given data set. In this approach, MCDM methods consider different numbers of clusters as alternatives and the outputs of any clustering algorithm on validity measures as criteria. The proposed method is examined by an experimental study using three MCDM methods, the well-known clustering algorithm–k-means, ten relative measures, and fifteen public-domain UCI machine learning data sets. The results show that MCDM methods work fairly well in estimating the number of clusters in the data and outperform the ten relative measures considered in the study.

Suggested Citation

  • Yi Peng & Yong Zhang & Gang Kou & Yong Shi, 2012. "A Multicriteria Decision Making Approach for Estimating the Number of Clusters in a Data Set," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-9, July.
    • Handle: RePEc:plo:pone00:0041713
    DOI: 10.1371/journal.pone.0041713
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0041713
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0041713&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0041713?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Glenn Milligan & Martha Cooper, 1985. "An examination of procedures for determining the number of clusters in a data set," Psychometrika, Springer;The Psychometric Society, vol. 50(2), pages 159-179, June.
    2. Peng, Yi & Kou, Gang & Wang, Guoxun & Shi, Yong, 2011. "FAMCDM: A fusion approach of MCDM methods to rank multiclass classification algorithms," Omega, Elsevier, vol. 39(6), pages 677-689, December.
    3. Robert Tibshirani & Guenther Walther & Trevor Hastie, 2001. "Estimating the number of clusters in a data set via the gap statistic," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 411-423.
    4. Sugar, Catherine A. & James, Gareth M., 2003. "Finding the Number of Clusters in a Dataset: An Information-Theoretic Approach," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 750-763, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Maghsoodi, Abtin Ijadi, 2023. "Cryptocurrency portfolio allocation using a novel hybrid and predictive big data decision support system," Omega, Elsevier, vol. 115(C).
    2. Zhiyong Li & Xinyi Hu & Ke Li & Fanyin Zhou & Feng Shen, 2020. "Inferring the outcomes of rejected loans: an application of semisupervised clustering," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(2), pages 631-654, February.
    3. Nilsen Gro & Borgan Ørnulf & LiestØl Knut & Lingjærde Ole Christian, 2013. "Identifying clusters in genomics data by recursive partitioning," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(5), pages 637-652, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Pai-Ling & Chiou, Jeng-Min, 2011. "Identifying cluster number for subspace projected functional data clustering," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2090-2103, June.
    2. J. Fernando Vera & Rodrigo Macías, 2021. "On the Behaviour of K-Means Clustering of a Dissimilarity Matrix by Means of Full Multidimensional Scaling," Psychometrika, Springer;The Psychometric Society, vol. 86(2), pages 489-513, June.
    3. Z. Volkovich & Z. Barzily & G.-W. Weber & D. Toledano-Kitai & R. Avros, 2012. "An application of the minimal spanning tree approach to the cluster stability problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(1), pages 119-139, March.
    4. Julian Rossbroich & Jeffrey Durieux & Tom F. Wilderjans, 2022. "Model Selection Strategies for Determining the Optimal Number of Overlapping Clusters in Additive Overlapping Partitional Clustering," Journal of Classification, Springer;The Classification Society, vol. 39(2), pages 264-301, July.
    5. Fischer, Aurélie, 2011. "On the number of groups in clustering," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1771-1781.
    6. Fang, Yixin & Wang, Junhui, 2012. "Selection of the number of clusters via the bootstrap method," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 468-477.
    7. Koltcov, Sergei, 2018. "Application of Rényi and Tsallis entropies to topic modeling optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 1192-1204.
    8. Jane L. Harvill & Priya Kohli & Nalini Ravishanker, 2017. "Clustering Nonlinear, Nonstationary Time Series Using BSLEX," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 935-955, September.
    9. Z. Volkovich & D. Toledano-Kitai & G.-W. Weber, 2013. "Self-learning K-means clustering: a global optimization approach," Journal of Global Optimization, Springer, vol. 56(2), pages 219-232, June.
    10. J. Fernando Vera & Rodrigo Macías, 2017. "Variance-Based Cluster Selection Criteria in a K-Means Framework for One-Mode Dissimilarity Data," Psychometrika, Springer;The Psychometric Society, vol. 82(2), pages 275-294, June.
    11. Lingsong Meng & Dorina Avram & George Tseng & Zhiguang Huo, 2022. "Outcome‐guided sparse K‐means for disease subtype discovery via integrating phenotypic data with high‐dimensional transcriptomic data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(2), pages 352-375, March.
    12. Fujita, André & Takahashi, Daniel Y. & Patriota, Alexandre G., 2014. "A non-parametric method to estimate the number of clusters," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 27-39.
    13. Yujia Li & Xiangrui Zeng & Chien‐Wei Lin & George C. Tseng, 2022. "Simultaneous estimation of cluster number and feature sparsity in high‐dimensional cluster analysis," Biometrics, The International Biometric Society, vol. 78(2), pages 574-585, June.
    14. Cyril Atkinson-Clement & Eléonore Pigalle, 2021. "What can we learn from Covid-19 pandemic’s impact on human behaviour? The case of France’s lockdown," Palgrave Communications, Palgrave Macmillan, vol. 8(1), pages 1-12, December.
    15. Kondo, Yumi & Salibian-Barrera, Matias & Zamar, Ruben, 2016. "RSKC: An R Package for a Robust and Sparse K-Means Clustering Algorithm," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 72(i05).
    16. Öttl, Gerald & Böck, Philipp & Werpup, Nadja & Schwarze, Malte, 2013. "Derivation of representative air traffic peaks as standard input for airport related simulation," Journal of Air Transport Management, Elsevier, vol. 28(C), pages 31-39.
    17. Oliver Schaer & Nikolaos Kourentzes & Robert Fildes, 2022. "Predictive competitive intelligence with prerelease online search traffic," Production and Operations Management, Production and Operations Management Society, vol. 31(10), pages 3823-3839, October.
    18. Fang, Yixin & Wang, Junhui, 2011. "Penalized cluster analysis with applications to family data," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2128-2136, June.
    19. Henner Gimpel & Daniel Rau & Maximilian Röglinger, 2018. "Understanding FinTech start-ups – a taxonomy of consumer-oriented service offerings," Electronic Markets, Springer;IIM University of St. Gallen, vol. 28(3), pages 245-264, August.
    20. J. Vera & Rodrigo Macías & Willem Heiser, 2013. "Cluster Differences Unfolding for Two-Way Two-Mode Preference Rating Data," Journal of Classification, Springer;The Classification Society, vol. 30(3), pages 370-396, October.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pone00:0041713. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.