Evidential multinomial logistic regression for multiclass classifier calibration

The calibration of classifiers is an important task in information fusion. To compare or combine the outputs of several classifiers, they need to be represented in a common space. Probabilistic calibration methods transform the output of a classifier into a posterior probability distribution. In this paper, we introduce an evidential calibration method for multiclass classification problems. Our approach uses an extension of multinomial logistic regression to the theory of belief functions. We demonstrate that the use of belief functions instead of probability distributions is often beneficial. In particular, when different classifiers are trained with unbalanced amount of training data, the gain achieved by our evidential approach can become significant. We applied our method to the calibration of multiclass SVM classifiers which were constructed through a 'one-vs-all' framework. Experiments were conducted using six different datasets from the UCI repository.