Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v101y2010i10p2464-2485.html
   My bibliography  Save this article

Projection-pursuit approach to robust linear discriminant analysis

Author

Listed:
  • Pires, Ana M.
  • Branco, João A.
Abstract
Discriminant analysis plays an important role in multivariate statistics as a prediction and classification method. It has been successfully applied in many fields of work and research. As it happens with other multivariate methods, discriminant analysis is highly vulnerable to the presence of outliers that commonly occur in many real world data sets. The lack of robustness of the classical estimators on which the linear discriminant function is based is a severe disadvantage and several authors have worked to find efficient ways to prevent the damage that outliers can cause. This paper focuses on the projection-pursuit approach to discriminant analysis. The projection-pursuit estimators are described and theoretical properties are deduced and their relevance is highlighted. These include Fisher consistency, affine equivariance, partial influence functions and asymptotic distributions. Application to real data and a simulation study reveal the robustness of the projection-pursuit approach. In both analyses the data relates to a large number of variables, a situation that is becoming common when new technology is applied to data gathering.

Suggested Citation

  • Pires, Ana M. & Branco, João A., 2010. "Projection-pursuit approach to robust linear discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2464-2485, November.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:10:p:2464-2485
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(10)00136-3
    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. Xu, Ping & Brock, Guy N. & Parrish, Rudolph S., 2009. "Modified linear discriminant analysis approaches for classification of high-dimensional microarray data," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1674-1687, March.
    2. Croux, Christophe & Joossens, Kristel, 2005. "Influence of observations on the misclassification probability in quadratic discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 384-403, October.
    3. Lee, Jae Won & Lee, Jung Bok & Park, Mira & Song, Seuck Heun, 2005. "An extensive comparison of recent classification tools applied to microarray data," Computational Statistics & Data Analysis, Elsevier, vol. 48(4), pages 869-885, April.
    4. Pires, Ana M. & Branco, João A., 2002. "Partial Influence Functions," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 451-468, November.
    5. N. A. Campbell, 1982. "Robust Procedures in Multivariate Analysis II. Robust Canonical Variate Analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(1), pages 1-8, March.
    6. Hubert, Mia & Van Driessen, Katrien, 2004. "Fast and robust discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 301-320, March.
    7. Croux, Christophe & Ruiz-Gazen, Anne, 2005. "High breakdown estimators for principal components: the projection-pursuit approach revisited," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 206-226, July.
    8. Todorov, Valentin & Neykov, Neyko & Neytchev, Plamen, 1994. "Robust two-group discrimination by bounded influence regression. A Monte Carlo simulation," Computational Statistics & Data Analysis, Elsevier, vol. 17(3), pages 289-302, March.
    9. He, Xuming & Fung, Wing K., 2000. "High Breakdown Estimation for Multiple Populations with Applications to Discriminant Analysis," Journal of Multivariate Analysis, Elsevier, vol. 72(2), pages 151-162, February.
    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. Kang, Xiaoning & Kang, Lulu & Chen, Wei & Deng, Xinwei, 2022. "A generative approach to modeling data with quantitative and qualitative responses," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    2. Bali, Juan Lucas & Boente, Graciela, 2017. "Robust estimators under a functional common principal components model," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 424-440.

    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. Todorov, Valentin & Filzmoser, Peter, 2009. "An Object-Oriented Framework for Robust Multivariate Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i03).
    2. Valentin Todorov, 2007. "Robust selection of variables in linear discriminant analysis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 395-407, February.
    3. Sajobi, Tolulope T. & Lix, Lisa M. & Dansu, Bolanle M. & Laverty, William & Li, Longhai, 2012. "Robust descriptive discriminant analysis for repeated measures data," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2782-2794.
    4. Bali, Juan Lucas & Boente, Graciela, 2017. "Robust estimators under a functional common principal components model," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 424-440.
    5. Todorov, Valentin & Filzmoser, Peter, 2010. "Robust statistic for the one-way MANOVA," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 37-48, January.
    6. Valentin Todorov, 2007. "Robust selection of variables in linear discriminant analysis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 395-407, February.
    7. Croux, Christophe & Joossens, Kristel, 2005. "Influence of observations on the misclassification probability in quadratic discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 384-403, October.
    8. Md. Matiur Rahaman & Md. Nurul Haque Mollah, 2019. "Robustification of Gaussian Bayes Classifier by the Minimum β-Divergence Method," Journal of Classification, Springer;The Classification Society, vol. 36(1), pages 113-139, April.
    9. Frénay, Benoît & Doquire, Gauthier & Verleysen, Michel, 2014. "Estimating mutual information for feature selection in the presence of label noise," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 832-848.
    10. Graciela Boente & Frank Critchley & Liliana Orellana, 2007. "Influence functions of two families of robust estimators under proportional scatter matrices," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 295-327, February.
    11. Bianco, Ana & Boente, Graciela & Pires, Ana M. & Rodrigues, Isabel M., 2008. "Robust discrimination under a hierarchy on the scatter matrices," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1332-1357, July.
    12. Boente, Graciela & Molina, Julieta & Sued, Mariela, 2010. "On the asymptotic behavior of general projection-pursuit estimators under the common principal components model," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 228-235, February.
    13. Mia Hubert & Stephan Van der Veeken, 2010. "Robust classification for skewed data," 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(4), pages 239-254, December.
    14. Matías Salibián-Barrera & Stefan Aelst & Gert Willems, 2008. "Fast and robust bootstrap," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(1), pages 41-71, February.
    15. Peter Filzmoser & Karel Hron & Matthias Templ, 2012. "Discriminant analysis for compositional data and robust parameter estimation," Computational Statistics, Springer, vol. 27(4), pages 585-604, December.
    16. Stefan Van Aelst & Gert Willems, 2010. "Inference for robust canonical variate analysis," 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 181-197, September.
    17. Salvador, B. & Fernandez, M.A. & Martin, I. & Rueda, C., 2008. "Robustness of classification rules that incorporate additional information," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2489-2495, January.
    18. Claudio Agostinelli & Luca Greco, 2019. "Weighted likelihood estimation of multivariate location and scatter," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 756-784, September.
    19. repec:jss:jstsof:32:i03 is not listed on IDEAS
    20. Huang, Yufen & Cheng, Ching-Ren & Wang, Tai-Ho, 2008. "Pair-perturbation influence functions of nongaussianity by projection pursuit," Computational Statistics & Data Analysis, Elsevier, vol. 52(8), pages 3971-3987, April.
    21. B. Barış Alkan, 2016. "Robust Principal Component Analysis Based on Modified Minimum Covariance Determinant in the Presence of Outliers," Alphanumeric Journal, Bahadir Fatih Yildirim, vol. 4(2), pages 85-94, September.

    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:101:y:2010:i:10:p:2464-2485. 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.