A multi-class logistic regression model for interval data

This paper introduces a new classifier based on the multi-class logistic regression model for interval symbolic data. Each example of the learning set is described by a feature vector, for which each feature value is an interval. Two versions of this classifier are considered. First fits a multi-class logistic regression model conjointly on the lower and upper bounds of the interval values assumed by the variables in the learning set. Second fits a multi-class logistic model on the lower and upper bounds separately. The prediction of the class for new examples is accomplished from the computation of the posterior probabilities of the classes. To show the usefulness of this method, examples with synthetic interval symbolic data sets with overlapping classes are considered. The assessment of the proposed classification method is based on the estimation of the average behaviour of the error rate in the framework of the Monte Carlo method.