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- Title
Discrimination of populations under covariance matrix heterogeneity and non-normal random vectors in genetic diversity studies.
- Authors
de CARVALHO, Vitor Prado; de SOUSA, Ithalo Coelho; NASCIMENTO, Moysés; NASCIMENTO, Ana Carolina Campana; CRUZ, Cosme Damião
- Abstract
Genetic diversity analysis has guided the choice of appropriate parents in breeding programs. Multivariate statistical methods such as discriminant analysis are used to obtain the necessary results in these studies. However, to obtain reliable results, one must meet assumptions such as covariance matrix heterogeneity and multivariate normality of the observation vector. Artificial Neural Network (ANN), Support Vector Machine (SVM), Decision Tree (DT) and its refinements do not have these assumptions and may be used in the choice of appropriate parents. This study evaluates the robustness of the Fisher's discriminant function under covariance matrix heterogeneity and multivariate non-normal random vectors. The results were compared with those obtained from Quadratic Discriminant Analysis (QDA), ANN, SVM and DT. Scenarios characterized by heterogeneous covariance matrices and multivariate non-normal random vectors were simulated. Considering the apparent error rate (APER), the SVM method (APER-Normal = 0.07; APER-Poisson = 0.13) and quadratic discriminant method (APER-Normal = 0.09; APER-Poisson = 0.09) presented better results for scenarios simulated with covariance matrix heteroscedasticity. For scenarios with multivariate normality and covariance matrix homoscedasticity, the SVM (APER = 0.15) and ANN (APER = 0.06) presented best results. For situations in which the data had multivariate Poisson distribution and covariance matrix homogeneity, the SVM (APER = 0.15), Fisher's discriminant function (APER = 0.19) and ANN (APER = 0.19) presented better performances. Finally, DT refinements (Bagging, Random Forest and Boosting) presented APER values less than 0.25 and are shown to be alternatives.
- Subjects
SUPPORT vector machines; ARTIFICIAL neural networks; DECISION trees; DISCRIMINANT analysis; POISSON distribution; COVARIANCE matrices
- Publication
Cientifica, 2018, Vol 46, Issue 4, p344
- ISSN
0100-0039
- Publication type
Article
- DOI
10.15361/1984-5529.2018v46n4p344-352