Parametric classification with soft labels using the evidential EM algorithm: linear discriminant analysis versus logistic regression

Partially supervised learning extends both supervised and unsupervised learning, by considering situations in which only partial information about the response variable is available. In this paper, we consider partially supervised classification and we assume the learning instances to be labeled by Dempster-Shafer mass functions, called soft labels. Linear discriminant analysis and logistic regression are considered as special cases of generative and discriminative parametric models. We show that the evidential EM algorithm can be particularized to fit the parameters in each of these models. We describe experimental results with simulated data sets as well as with two real applications: K-complex detection in sleep EEGs signals and facial expression recognition. These results confirm the interest of using soft labels for classification as compared to potentially erroneous crisp labels, when the true class membership is partially unknown or ill-defined.