The unimodal model for the classification of ordinal data

Many real life problems require the classification of items into naturally ordered classes. These problems are traditionally handled by conventional methods intended for the classification of nominal classes where the order relation is ignored. This paper introduces a new machine learning paradigm intended for multi-class classification problems where the classes are ordered. The theoretical development of this paradigm is carried out under the key idea that the random variable class associated with a given query should follow a unimodal distribution. In this context, two approaches are considered: a parametric, where the random variable class is assumed to follow a specific discrete distribution; a nonparametric, where the random variable class is assumed to be distribution-free. In either case, the unimodal model can be implemented in practice by means of feedforward neural networks and support vector machines, for instance. Nevertheless, our main focus is on feedforward neural networks. We also introduce a new coefficient, rint, to measure the performance of ordinal data classifiers. An experimental study with artificial and real datasets is presented in order to illustrate the performances of both parametric and nonparametric approaches and compare them with the performances of other methods. The superiority of the parametric approach is suggested, namely when flexible discrete distributions, a new concept introduced here, are considered.