Fig. 1.

Schematic example of the classification problem in a 2D space in the presence of mislabeled examples and unknown sub-classes. Dark blue dots correspond to good responders and light red dots to bad responders. With a supervised training of a classifier with two HMMs (a), the mislabeled examples are mistakenly assigned to the class indicated by the wrong label which leads to higher SD in the respective model parameters, thereby weakening the predictive power of the model. Our approach, which uses the negative constraints (dashed lines) to guide the training (b), allows the mislabeled patients to be assigned to the closest HMM, if the assignment improves the overall model likelihood, leading to more discriminative parameters. In other words, the soft negative constraints resulting from wrongly labeled patients are overruled if this leads to improved overall model likelihood. Exploring the existence of sub-classes, as in the case of three HMMs depicted in (c), can further improve class discrimination.