IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v54y2010i9p2113-2127.html
   My bibliography  Save this article

James-Stein shrinkage to improve k-means cluster analysis

Author

Listed:
  • Gao, Jinxin
  • Hitchcock, David B.

Abstract

We study a general algorithm to improve the accuracy in cluster analysis that employs the James-Stein shrinkage effect in k-means clustering. We shrink the centroids of clusters toward the overall mean of all data using a James-Stein-type adjustment, and then the James-Stein shrinkage estimators act as the new centroids in the next clustering iteration until convergence. We compare the shrinkage results to the traditional k-means method. A Monte Carlo simulation shows that the magnitude of the improvement depends on the within-cluster variance and especially on the effective dimension of the covariance matrix. Using the Rand index, we demonstrate that accuracy increases significantly in simulated data and in a real data example.

Suggested Citation

  • Gao, Jinxin & Hitchcock, David B., 2010. "James-Stein shrinkage to improve k-means cluster analysis," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2113-2127, September.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:9:p:2113-2127
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(10)00120-9
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Bénédicte Vidaillet & V. d'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL.
    2. Krzanowski, Wojtek J. & Hand, David J., 2009. "A simple method for screening variables before clustering microarray data," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2747-2753, May.
    3. J. A. Cuesta‐Albertos & C. Matrán & A. Mayo‐Iscar, 2008. "Robust estimation in the normal mixture model based on robust clustering," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 779-802, September.
    4. Wayne DeSarbo & J. Carroll & Linda Clark & Paul Green, 1984. "Synthesized clustering: A method for amalgamating alternative clustering bases with differential weighting of variables," Psychometrika, Springer;The Psychometric Society, vol. 49(1), pages 57-78, March.
    5. L. A. García‐Escudero & A. Gordaliza & R. San Martín & S. Van Aelst & R. Zamar, 2009. "Robust linear clustering," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 301-318, January.
    6. Hitchcock, David B. & Chen, Zhimin, 2008. "Smoothing dissimilarities to cluster binary data," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4699-4711, June.
    7. Douglas Steinley & Michael Brusco, 2008. "Selection of Variables in Cluster Analysis: An Empirical Comparison of Eight Procedures," Psychometrika, Springer;The Psychometric Society, vol. 73(1), pages 125-144, March.
    8. Michael Brusco & J. Cradit, 2001. "A variable-selection heuristic for K-means clustering," Psychometrika, Springer;The Psychometric Society, vol. 66(2), pages 249-270, June.
    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. Tiefeng Ma & Shuangzhe Liu & S. Ahmed, 2014. "Shrinkage estimation for the mean of the inverse Gaussian population," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(6), pages 733-752, August.
    2. Brentnall, Adam R. & Crowder, Martin J. & Hand, David J., 2011. "Approximate repeated-measures shrinkage," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1150-1159, February.

    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. Pacheco, Joaquín & Casado, Silvia & Porras, Santiago, 2013. "Exact methods for variable selection in principal component analysis: Guide functions and pre-selection," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 95-111.
    2. Tsai, Chieh-Yuan & Chiu, Chuang-Cheng, 2008. "Developing a feature weight self-adjustment mechanism for a K-means clustering algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4658-4672, June.
    3. Susan Brudvig & Michael J. Brusco & J. Dennis Cradit, 2019. "Joint selection of variables and clusters: recovering the underlying structure of marketing data," Journal of Marketing Analytics, Palgrave Macmillan, vol. 7(1), pages 1-12, March.
    4. Brusco, Michael J. & Steinley, Douglas, 2011. "Exact and approximate algorithms for variable selection in linear discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 123-131, January.
    5. Michael Brusco & Renu Singh & Douglas Steinley, 2009. "Variable Neighborhood Search Heuristics for Selecting a Subset of Variables in Principal Component Analysis," Psychometrika, Springer;The Psychometric Society, vol. 74(4), pages 705-726, December.
    6. Luis García-Escudero & Alfonso Gordaliza & Carlos Matrán & Agustín Mayo-Iscar, 2010. "A review of robust clustering methods," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 4(2), pages 89-109, September.
    7. Douglas Steinley & Michael Brusco, 2008. "Selection of Variables in Cluster Analysis: An Empirical Comparison of Eight Procedures," Psychometrika, Springer;The Psychometric Society, vol. 73(1), pages 125-144, March.
    8. Maarten M. Kampert & Jacqueline J. Meulman & Jerome H. Friedman, 2017. "rCOSA: A Software Package for Clustering Objects on Subsets of Attributes," Journal of Classification, Springer;The Classification Society, vol. 34(3), pages 514-547, October.
    9. Naoto Yamashita & Kohei Adachi, 2020. "A Modified k-Means Clustering Procedure for Obtaining a Cardinality-Constrained Centroid Matrix," Journal of Classification, Springer;The Classification Society, vol. 37(2), pages 509-525, July.
    10. Douglas L. Steinley, 2016. "Editorial," Journal of Classification, Springer;The Classification Society, vol. 33(2), pages 167-170, July.
    11. van Dijk, Dick & Hans Franses, Philip & Peter Boswijk, H., 2007. "Absorption of shocks in nonlinear autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4206-4226, May.
    12. Robert Lehmann & Antje Weyh, 2016. "Forecasting Employment in Europe: Are Survey Results Helpful?," Journal of Business Cycle Research, Springer;Centre for International Research on Economic Tendency Surveys (CIRET), vol. 12(1), pages 81-117, September.
    13. Yao, Weixin & Wei, Yan & Yu, Chun, 2014. "Robust mixture regression using the t-distribution," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 116-127.
    14. Cubadda, Gianluca & Hecq, Alain & Palm, Franz C., 2009. "Studying co-movements in large multivariate data prior to multivariate modelling," Journal of Econometrics, Elsevier, vol. 148(1), pages 25-35, January.
    15. Sucarrat, Genaro & Grønneberg, Steffen & Escribano, Alvaro, 2016. "Estimation and inference in univariate and multivariate log-GARCH-X models when the conditional density is unknown," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 582-594.
    16. Guérin, Pierre & Maurin, Laurent & Mohr, Matthias, 2015. "Trend-Cycle Decomposition Of Output And Euro Area Inflation Forecasts: A Real-Time Approach Based On Model Combination," Macroeconomic Dynamics, Cambridge University Press, vol. 19(2), pages 363-393, March.
    17. Mauro Costantini & Ulrich Gunter & Robert M. Kunst, 2017. "Forecast Combinations in a DSGE‐VAR Lab," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 36(3), pages 305-324, April.
    18. Krätschell, Karoline & Schmidt, Torsten, 2013. "Long-run trends or short-run fluctuations What establishes the correlation between oil and food prices?," VfS Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79798, Verein für Socialpolitik / German Economic Association.
    19. Ana María Iregui & Jesús Otero, 2013. "A Spatiotemporal Analysis of Agricultural Prices: An Application to Colombian Data," Agribusiness, John Wiley & Sons, Ltd., vol. 29(4), pages 497-508, September.
    20. Cudjoe, Godsway & Breisinger, Clemens & Diao, Xinshen, 2010. "Local impacts of a global crisis: Food price transmission, consumer welfare and poverty in Ghana," Food Policy, Elsevier, vol. 35(4), pages 294-302, August.

    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:eee:csdana:v:54:y:2010:i:9:p:2113-2127. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.