title: Genome-enabled prediction using probabilistic neural network classifiers.
abstract: BACKGROUND
  Multi-layer perceptron (MLP) and radial basis function neural networks (RBFNN) have been shown to be effective in genome-enabled prediction. Here, we evaluated and compared the classification performance of an MLP classifier versus that of a probabilistic neural network (PNN), to predict the probability of membership of one individual in a phenotypic class of interest, using genomic and phenotypic data as input variables. We used 16 maize and 17 wheat genomic and phenotypic datasets with different trait-environment combinations (sample sizes ranged from 290 to 300 individuals) with 1.4 k and 55 k SNP chips. Classifiers were tested using continuous traits that were categorized into three classes (upper, middle and lower) based on the empirical distribution of each trait, constructed on the basis of two percentiles (15-85 % and 30-70 %). We focused on the 15 and 30 % percentiles for the upper and lower classes for selecting the best individuals, as commonly done in genomic selection. Wheat datasets were also used with two classes. The criteria for assessing the predictive accuracy of the two classifiers were the area under the receiver operating characteristic curve (AUC) and the area under the precision-recall curve (AUCpr). Parameters of both classifiers were estimated by optimizing the AUC for a specific class of interest.
  
  
  RESULTS
  The AUC and AUCpr criteria provided enough evidence to conclude that PNN was more accurate than MLP for assigning maize and wheat lines to the correct upper, middle or lower class for the complex traits analyzed. Results for the wheat datasets with continuous traits split into two and three classes showed that the performance of PNN with three classes was higher than with two classes when classifying individuals into the upper and lower (15 or 30 %) categories.
  
  
  CONCLUSIONS
  The PNN classifier outperformed the MLP classifier in all 33 (maize and wheat) datasets when using AUC and AUCpr for selecting individuals of a specific class. Use of PNN with Gaussian radial basis functions seems promising in genomic selection for identifying the best individuals. Categorizing continuous traits into three classes generally provided better classification than when using two classes, because classification accuracy improved when classes were balanced.
authors.affiliation: Colegio de Postgraduados, Campus Montecillo, Texcoco, México, 056230, México. jmgc@colpos.mx.
authors.forename: Juan Manuel
authors.initials: JM
authors.lastname: González-Camacho
authors.affiliation: Biometrics and Statistics Unit (BSU), International Maize and Wheat Improvement Center (CIMMYT), Apdo Postal 6-641, México DF, 06600 24105, México. j.crossa@cgiar.org.
authors.forename: José
authors.initials: J
authors.lastname: Crossa
authors.affiliation: Colegio de Postgraduados, Campus Montecillo, Texcoco, México, 056230, México. perpdgo@gmail.com.
authors.forename: Paulino
authors.initials: P
authors.lastname: Pérez-Rodríguez
authors.affiliation: NIDERA SEMILLAS S.A., Ruta 8 Km. 376, 2600, Venado Tuerto, Argentina. leonardoornella@gmail.com.
authors.forename: Leonardo
authors.initials: L
authors.lastname: Ornella
authors.affiliation: Department of Animal Sciences, University of Wisconsin, Madison, 53706, USA. gianola@ansci.wisc.edu.
authors.forename: Daniel
authors.initials: D
authors.lastname: Gianola
mesh_terms: D019540:Area Under Curve; D059647:Gene-Environment Interaction; D023281:Genomics / Q000379:methods*; D008957:Models, Genetic; D016571:Neural Networks, Computer; D010641:Phenotype; D020641:Polymorphism, Single Nucleotide; D012372:ROC Curve; D014908:Triticum / Q000235:genetics*; D003313:Zea mays / Q000235:genetics*