IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v65y2024i2d10.1007_s00362-023-01411-6.html
   My bibliography  Save this article

Clustering and estimation of finite mixture models under bivariate ranked set sampling with application to a breast cancer study

Author

Listed:
  • Hamid Haji Aghabozorgi

    (Allameh Tabataba’i University)

  • Farzad Eskandari

    (Allameh Tabataba’i University)

Abstract

In the literature on modeling heterogeneous data via mixture models, it is generally assumed that the samples are drawn from the underlying population using the simple random sampling (SRS) technique. This study exploits the bivariate ranked set sampling (BVRSS) technique to learn finite mixture models. We generalize the expectation-maximization (EM) algorithm under univariate RSS to the bivariate case. Computationally, through a simulation study under a noisy setting, we compare the performance of the proposed rank-based estimators with that of the SRS-based competitors in estimating unknown parameters and cluster assignments. The proposed methodology is applied to a breast cancer data set to diagnose malignant or benign tumors in patients. The results showed that the extra rank information in BVRSS samples leads to a better inference about the unknown features of mixture models.

Suggested Citation

  • Hamid Haji Aghabozorgi & Farzad Eskandari, 2024. "Clustering and estimation of finite mixture models under bivariate ranked set sampling with application to a breast cancer study," Statistical Papers, Springer, vol. 65(2), pages 705-736, April.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:2:d:10.1007_s00362-023-01411-6
    DOI: 10.1007/s00362-023-01411-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-023-01411-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-023-01411-6?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. Olvi L. Mangasarian & W. Nick Street & William H. Wolberg, 1995. "Breast Cancer Diagnosis and Prognosis Via Linear Programming," Operations Research, INFORMS, vol. 43(4), pages 570-577, August.
    2. Armin Hatefi & Mohammad Jafari Jozani & Omer Ozturk, 2015. "Mixture Model Analysis of Partially Rank-Ordered Set Samples: Age Groups of Fish from Length-Frequency Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 848-871, September.
    3. Hatefi, Armin & Jafari Jozani, Mohammad, 2013. "Fisher information in different types of perfect and imperfect ranked set samples from finite mixture models," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 16-31.
    Full references (including those not matched with items on IDEAS)

    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. Sexton, Randall S. & Dorsey, Robert E. & Johnson, John D., 1999. "Optimization of neural networks: A comparative analysis of the genetic algorithm and simulated annealing," European Journal of Operational Research, Elsevier, vol. 114(3), pages 589-601, May.
    2. Brandner, Hubertus & Lessmann, Stefan & Voß, Stefan, 2013. "A memetic approach to construct transductive discrete support vector machines," European Journal of Operational Research, Elsevier, vol. 230(3), pages 581-595.
    3. W. Art Chaovalitwongse & Ya-Ju Fan & Rajesh C. Sachdeo, 2008. "Novel Optimization Models for Abnormal Brain Activity Classification," Operations Research, INFORMS, vol. 56(6), pages 1450-1460, December.
    4. Tamilselvan, Prasanna & Wang, Pingfeng, 2013. "Failure diagnosis using deep belief learning based health state classification," Reliability Engineering and System Safety, Elsevier, vol. 115(C), pages 124-135.
    5. Yaqiong Cui & Jukka Sirén & Timo Koski & Jukka Corander, 2016. "Simultaneous Predictive Gaussian Classifiers," Journal of Classification, Springer;The Classification Society, vol. 33(1), pages 73-102, April.
    6. Ramazan Ünlü & Petros Xanthopoulos, 2019. "A weighted framework for unsupervised ensemble learning based on internal quality measures," Annals of Operations Research, Springer, vol. 276(1), pages 229-247, May.
    7. Morris, Katherine & McNicholas, Paul D., 2016. "Clustering, classification, discriminant analysis, and dimension reduction via generalized hyperbolic mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 133-150.
    8. Ryu, Young U. & Chandrasekaran, R. & Jacob, Varghese S., 2007. "Breast cancer prediction using the isotonic separation technique," European Journal of Operational Research, Elsevier, vol. 181(2), pages 842-854, September.
    9. B Baesens & C Mues & D Martens & J Vanthienen, 2009. "50 years of data mining and OR: upcoming trends and challenges," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 16-23, May.
    10. Sahin, Özge & Czado, Claudia, 2022. "Vine copula mixture models and clustering for non-Gaussian data," Econometrics and Statistics, Elsevier, vol. 22(C), pages 136-158.
    11. A. Astorino & M. Gaudioso, 2002. "Polyhedral Separability Through Successive LP," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 265-293, February.
    12. Alejandro Murua & Nicolas Wicker, 2015. "Kernel-based mixture models for classification," Computational Statistics, Springer, vol. 30(2), pages 317-344, June.
    13. Pedro Duarte Silva, A., 2017. "Optimization approaches to Supervised Classification," European Journal of Operational Research, Elsevier, vol. 261(2), pages 772-788.
    14. Sung, Bongjung & Lee, Jaeyong, 2023. "Covariance structure estimation with Laplace approximation," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    15. Wang, Wan-Lun, 2015. "Mixtures of common t-factor analyzers for modeling high-dimensional data with missing values," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 223-235.
    16. Wang, Haifeng & Zheng, Bichen & Yoon, Sang Won & Ko, Hoo Sang, 2018. "A support vector machine-based ensemble algorithm for breast cancer diagnosis," European Journal of Operational Research, Elsevier, vol. 267(2), pages 687-699.
    17. Jun-Ya Gotoh & Michael Jong Kim & Andrew E. B. Lim, 2017. "Calibration of Distributionally Robust Empirical Optimization Models," Papers 1711.06565, arXiv.org, revised May 2020.
    18. Xin Liu & Bangxin Zhao & Wenqing He, 2020. "Simultaneous Feature Selection and Classification for Data-Adaptive Kernel-Penalized SVM," Mathematics, MDPI, vol. 8(10), pages 1-22, October.
    19. Eva K. Lee & Richard J. Gallagher & David A. Patterson, 2003. "A Linear Programming Approach to Discriminant Analysis with a Reserved-Judgment Region," INFORMS Journal on Computing, INFORMS, vol. 15(1), pages 23-41, February.
    20. W. N. Street & O. L. Mangasarian, 1998. "Improved Generalization via Tolerant Training," Journal of Optimization Theory and Applications, Springer, vol. 96(2), pages 259-279, February.

    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:spr:stpapr:v:65:y:2024:i:2:d:10.1007_s00362-023-01411-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.