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Vector quantization and clustering in the presence of censoring

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  • 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
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    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.
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    3. 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.
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    5. 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.
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    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.

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