IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v140y2015icp220-233.html
   My bibliography  Save this article

Vector quantization and clustering in the presence of censoring

Author

Listed:
  • Gribkova, Svetlana

Abstract

We consider the problem of optimal vector quantization for random vectors with one censored component and applications to clustering of censored observations. We introduce the definitions of the empirical distortion and of the empirically optimal quantizer in the presence of censoring and we establish the almost sure consistency of empirical design. Moreover, we provide a non asymptotic exponential bound for the difference between the performance of the empirically optimal k-quantizer and the optimal performance over the class of all k-quantizers. As a natural application of the new quantization criterion, we propose an iterative two-step algorithm allowing for clustering of multivariate observations with one censored component. This method is investigated numerically through applications to real and simulated data.

Suggested Citation

  • Gribkova, Svetlana, 2015. "Vector quantization and clustering in the presence of censoring," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 220-233.
    • Handle: RePEc:eee:jmvana:v:140:y:2015:i:c:p:220-233
    DOI: 10.1016/j.jmva.2015.05.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X15001426
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2015.05.015?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
    ---><---

    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. César Sánchez Sellero & Wenceslao González Manteiga & Ingrid Van Keilegom, 2005. "Uniform Representation of Product‐Limit Integrals with Applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(4), pages 563-581, December.
    2. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    3. Stute, W., 1993. "Consistent Estimation Under Random Censorship When Covariables Are Present," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 89-103, April.
    4. A. Gannoun & Jérôme Saracco & K. Yu, 2007. "Comparison of kernel estimators of conditional distribution function and quantile regression under censoring for survival analysis," Post-Print hal-00153550, HAL.
    5. 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.
    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. Dash, Rasmita & Misra, Bijan Bihari, 2018. "Performance analysis of clustering techniques over microarray data: A case study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 162-176.

    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. Ana Helena Tavares & Jakob Raymaekers & Peter J. Rousseeuw & Paula Brito & Vera Afreixo, 2020. "Clustering genomic words in human DNA using peaks and trends of distributions," 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. 14(1), pages 57-76, March.
    3. Wang, Ketong & Porter, Michael D., 2018. "Optimal Bayesian clustering using non-negative matrix factorization," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 395-411.
    4. Douglas L. Steinley & M. J. Brusco, 2019. "Using an Iterative Reallocation Partitioning Algorithm to Verify Test Multidimensionality," Journal of Classification, Springer;The Classification Society, vol. 36(3), pages 397-413, October.
    5. Hennig, Christian, 2008. "Dissolution point and isolation robustness: Robustness criteria for general cluster analysis methods," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1154-1176, July.
    6. 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.
    7. Jacobo Uña-Álvarez & Noël Veraverbeke, 2013. "Generalized copula-graphic estimator," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 343-360, June.
    8. Michael Brusco & Douglas Steinley, 2015. "Affinity Propagation and Uncapacitated Facility Location Problems," Journal of Classification, Springer;The Classification Society, vol. 32(3), pages 443-480, October.
    9. Boztug, Yasemin & Reutterer, Thomas, 2008. "A combined approach for segment-specific market basket analysis," European Journal of Operational Research, Elsevier, vol. 187(1), pages 294-312, May.
    10. Zhiguang Huo & Li Zhu & Tianzhou Ma & Hongcheng Liu & Song Han & Daiqing Liao & Jinying Zhao & George Tseng, 2020. "Two-Way Horizontal and Vertical Omics Integration for Disease Subtype Discovery," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 12(1), pages 1-22, April.
    11. Olivier Lopez & Xavier Milhaud & Pierre-Emmanuel Thérond, 2016. "Tree-based censored regression with applications in insurance," Post-Print hal-01141228, HAL.
    12. Olivier Lopez & Valentin Patilea, 2007. "Nonparametric Lack-of-fit Tests for Parametric Mean-Regression Model with Censored Data," Working Papers 2007-01, Center for Research in Economics and Statistics.
    13. Wang, Xiaogang & Qiu, Weiliang & Zamar, Ruben H., 2007. "CLUES: A non-parametric clustering method based on local shrinking," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 286-298, September.
    14. 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.
    15. Michio Yamamoto, 2012. "Clustering of functional data in a low-dimensional subspace," 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. 6(3), pages 219-247, October.
    16. Weinand, J.M. & McKenna, R. & Fichtner, W., 2019. "Developing a municipality typology for modelling decentralised energy systems," Utilities Policy, Elsevier, vol. 57(C), pages 75-96.
    17. Lopez, O. & Patilea, V., 2009. "Nonparametric lack-of-fit tests for parametric mean-regression models with censored data," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 210-230, January.
    18. Dario Bruzzese & Domenico Vistocco, 2015. "DESPOTA: DEndrogram Slicing through a PemutatiOn Test Approach," Journal of Classification, Springer;The Classification Society, vol. 32(2), pages 285-304, July.
    19. Kohei Uno & Kohei Adachi & Nickolay T. Trendafilov, 2019. "Clustered Common Factor Exploration in Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 84(4), pages 1048-1067, December.
    20. Fabrizio Durante & Roberta Pappadà & Nicola Torelli, 2014. "Clustering of financial time series in risky scenarios," 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. 8(4), pages 359-376, December.

    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:jmvana:v:140:y:2015:i:c:p:220-233. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.