Comparing the Performance of Zero Mean Classification Functions under Unequal Misclassification Cost

Michael Asamoah-Boaheng^1, , Atinuke O. Adebanji² and Nkansah Ababio³

¹School of Graduate Studies Research and Innovation, Kumasi Polytechnic, Box 854, Kumasi, Ghana

²Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana

³Kofi Agyei Senior High School, P.O Box AN 2471 Ash-Town Kumasi, Bampenase-Ashanti

Cite this paper

Michael Asamoah-Boaheng, Atinuke O. Adebanji and Nkansah Ababio. Comparing the Performance of Zero Mean Classification Functions under Unequal Misclassification Cost. American Journal of Applied Mathematics and Statistics. 2014; 2(6):409-415. doi: 10.12691/AJAMS-2-6-9

Abstract

In this study the performance of Minimum Expected Cost of Misclassification method (MECM) and Quadratic Discriminant Function approach (QDF) were compared and evaluated for the case of equal mean discrimination under unequal misclassification cost. 30 pairs of Female liked sex twins extracted from Stocks (1933) ten (10) variate data on 832 twin children was used for evaluation. Discriminant functions were derived under each of the following misclassification cost ratios; 1: 1, 1: 2, 1: 3 and 1: 4 and their error rate estimates determined using the Cross Validation (CV) and Balanced Error Rate (BER) methods. Least Mean error rates were recorded under QDF method as compared to that of MECM. The error rate estimates showed the QDF outperforming the MECM in the provision of maximum separation between the two groups. Also the two classification rules were found to be sensitive to misclassification cost ratios exceeding 1:2.

Keywords

classification rules, error rates, discriminant functions, minimum expected cost of misclassification

Copyright

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References

[1]	Adebanji, A.O., Adeyemi, S., and Iyaniwura, J.O., “Effect of sample size Ratio on the Performance of the Linear Discriminate function”, International Journal of Modern Mathematics 3 (1), 97-108. 2008.
[2]	Ariyo, O.S., and Adebanji, A.O, “Effect of Misclassification Costs on the Performance Functions”, Paper Presented at the 45th Annual Conference of the Science Association of Nigeria (SAN) held Niger Delta University, Wilberforce, Island, Bayelsa State, 2010.
[3]	Bartlett, M.S., and Please, N.W., “Discrimination in the case of zero mean differences. Biometrika, 50 (1/2): 17-21. 1963.
[4]	Desu, M.M. and Geisser, S., “Methods and applications of equal-mean discrimination”, Discriminant Analysis and Applications, pages 139-161. 1973.
[5]	Fisher, R.A., “The Use of Multiple Measurements in Taxonomic Problems”, Annals of Eungenics, 7, 179-188. 1936.
[6]	Ganeslingam, S., Nanthakumar, A., and Ganesh, S., “A comparison of quadratic discriminant function with discriminant function based on absolute deviation from the mean”, Journal of Statistics and Management Studies, 9:441-457. 2006.
[7]	Geisser, S. and Desu, M.M., “Predictive zero-mean uniform discrimination”, Biometrika, 55, No. 3: 519-524. 1968
[8]	Hyodo, M. and Kubokawa, T., “A variable selection criterion for linear discriminant rule and its optimality in high dimensional and large sample data”, Journal of multivariate Analysis, 123, 364-379. 2014
[9]	Johnson, R.A. and Wichern, D.W., Applied Multivariate Statistical Analysis, (Sixth ed). NJ: Pearson Education, Inc. 575-621. 2007.
[10]	Lachenbruch, P.A., “Zero-mean difference discrimination and the absolute linear discriminant function”, Biometrika, 62 (2): 397-401. 1975.
[11]	Maharaj, E.A., Alonso, A.M., “Discriminant analysis of multivariate time series: Application to diagnosis based on ECG signals”, Computational Statistics and Data Analysis, 70 (2014): 67-87. 2014.
[12]	Marco, V.R.., Young, D.M., and Tubne, D.W., “Asymptotic expansions and estimation of the expected error rate for equal-mean discrimination with uniform covariance structure”, Biometrika, 29 (1): 103-111. 1987.
[13]	Okamoto, M., “Discrimination for variance matrices. Osaka Math., 13: 1-39. 1961.
[14]	Stocks, P., “A biometric investigation of twins, Part II”, Ann. Eugen, 5, 1-55. 1933.