Multinomial logistic regression and product unit neural network models: Application of a new hybrid methodology for solving a classification problem in the livestock sector

This work presents a new approach for multi-class pattern recognition based on the hybridization of a linear and nonlinear model. We propose multinomial logistic regression where some new covariates are defined by a product unit neural network, where in turn, the nonlinear basis functions are constructed with the product of the inputs raised to arbitrary powers. The application of this methodology involves, first of all, training the coefficients and the basis structure of product unit models using techniques based on artificial neural networks and evolutionary algorithms, followed by the application of multinomial logistic regression to both the new derived features and the original ones. To evaluate the efficacy of our technique we pose a difficult problem, the classification of sheep with respect to their milk production in different lactations, using covariates that only involve the first weeks of lactation. This enables the productive capacity of the animal to be identified more rapidly and leads to a faster selection process in determining the best producers. The results obtained with our approach are compared to other classification methodologies. Although several of these methodologies offer good results, the percentage of cases correctly classified was higher with our approach, which shows how instrumental the potential use of this methodology is for decision making in livestock enterprises, a sector relatively untouched by the technological innovations in business management that have been appearing in the last few years.