Comparative Linear Classification Splicing
The conventional Fisher linear classification analysis has been investigated by numerous researchers and this has led to different modification or splicing due to non- robustness when the assumptions are violated and also when the data set contains influential observations. This paper adduced a winsorized procedure to robustify the probability base classification approach. The comparative classification performance of the Fisher linear classification analysis and its spliced versions when the data set are contaminated are investigated. The simulation results revealed that the robust Fisherâ€™s approach based on the minimum covariance determinant estimates outperformed the other procedures; a good competitor to this technique is the winsorized probability base classification technique. Though, the robust Fisherâ€™s technique using the minimum covariance determinant estimates breakdown for mixture contamination. On a general note, the conventional Fisherâ€™s approach and the probability base technique performed comparable.
Chiang, L. H., Kotanchek, M. E., and Kordon, A. K., 2004, Fault diagnosis based on Fisher discriminant analysis and support vector machines, Computer and Chemical Engineer 28, 1389-1401.
Crimin, K., McKean, J. W., and Sheather, S. J., 2007, Discriminant procedures based on efficient robust discriminant coordinates, journal of nonparametric statistics 9, 199-213.
Croux, C., and Haesbroeck, G.,, 1999, Influence function and efficiency of the minimum covariance determinant scatter matrix estimator, Journal of multivariate analysis 71, 161-190.
Croux, C., and Haesbroeck, G., , 2000, Principal component analysis based on robust estimators of the covariance or correlation matrix: Influence functions and efficiencies, Biometrika 87, 603-618.
Croux, C., Filzmoser, P., and Joossens, K., 2008, Classification efficiencies for robust linear discriminant analysis, Statistica Sinica 18, 581-599.
Fauconnier, G., and Haesbroeck, G.,, 2009, Outliers detection with minimum covariance determinant estimator in practice, Statistical methodology 6, 363-379.
Gervini, D., 2003, A robust and efficient adaptive reweighted estimator of multivariate location and scatter, Journal of multivariate analysis 84, 116-144.
Hawkins, D. M., and Mclachlan, G. J.,, 1997, High breakdown linear discriminant analysis, Journal of the American Statistical Association 92, 136-143.
Hubert, M., and Van Driessen, K., 2004a, Fast and robust discriminant analysis, Computational Statistics and Data Analysis 45, 301-320.
Hubert, M., and Van Driessen, K.,, 2004b, Fast and robust discriminant analysis, Computational Statistics and Data Analysis 45, 301-320.
Hubert, M., Rousseeuw, P. J., and Van Aelst, S.,, 2008, High breakdown robust multivariate methods, Statistical Science 23, 92-119.
Hubert, M., Rousseeuw, P. J., and Verdonck, T., 2011a, A deterministic algorithm for the MCD, Citeseerx.ist.psu.edu/viewdoc/summary?, 1-26.
Hubert, M., Rousseeuw, P. J., and Verdonck, T.,. 2011b, A deterministic algorithm for the MCD.
Johnson, R. A., and Wichern, D. W., 2007, Applied multivariate statistical analysis (Pearson Prentice Hall, Upper Saddle River.
Khan, J. A., Van Aelst, S. and Zamar, H. R., 2007, Robust linear model selection based on least angle regression, Journal of the American Statistiscal Association 102, 1289-1299.
Maronna, R., Martin, R. D., and Yohai, V. J.,, 2006, Robust statistics: Theory and methods (John Wiley, New York.
Munoz-Pichardo, J. M., Enguix-Gonzalez, A., Munoz -Garcia, J., and Moreno-Rebollo, J.L.,, 2011, Influence analysis on discriminant coordinates, Communications in statistics-simulation and computation 40, 793-807.
Okwonu, F. Z., and Othman, A. R., 2013, Probability base classification technique: A preliminary study for two groups, Journal of Mathematical Theory and Model 3, 40-46.
Okwonu, F. Z., 2016. Supervised difference linear classification techniques for two group's problem. Nigerian Journal of Science and Environment,Vol.13 (1), 111-116.
Okwonu, F.Z., 2013. Comparison of several robust unbiased linear classification techniques for two groups. Unpublished manuscript, USM.
Pison, G., Van Aelst, S., and Willems, G.,, 2002, Small sample corrections fot LTS and MCD, Metrika 55, 111-123.
Pohar, M., Blas, M., and Turk. S., 2004, Comparison of logistic regression and linear discriminant analysis: A simulation study, Metodoloski zvezki 1, 143-161.
Rencher, A. C., 2002, A methods of multivariate analysis (A John Wiley & Sons, Inc.
Rousseeuw P. J., 1985, Multivariate Estimators With High Breakdown Point, Mathematical Statistics and its Applications B, 283-297.
Rousseeuw, P. J., and Van Driessen, K., 1999a, A fast algorithm for the minimum covariance determinant estimator, Technometrics 41, 212-223.
Rousseeuw, P. J., and Van Driessen, K.,, 1999b, A fast algorithm for the minimum covariance determinant estimator, Technometrics 41, 212-223.
Rousseeuw, P. J., and Van Zomeren, B. C.,, 1990, Unmasking multivariate outliers and leverage points, Journal of the American Statistical Association 85, 633-651.
Wang, D., and Romagnoli, J. A., 2005, A robust discriminate analysis method for process fault diagnosis, European Symposium on Computed Aided Process Engineering-15, 1-6.
Wang, Y., Zhang, Y.,Yi, J., Qu, H., and Miu, J., 2014, A robust probability classifier based on the modified x2 - distance, Mathematical Problems in Engineering 2014, 1-11.
Wilcox, R. R., and Keselman, H. J., 2003, Modern robust data analysis method: Measures of central tendency, Psychological Methods 8, 254-274.
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