Learning partial ordinal class memberships with kernel-based proportional odds models

As an extension of multi-class classification, machine learning algorithms have been proposed that are able to deal with situations in which the class labels are defined in a non-crisp way. Objects exhibit in that sense a degree of membership to several classes. In a similar setting, models are developed here for classification problems where an order relation is specified on the classes (i.e., non-crisp ordinal regression problems). As for traditional (crisp) ordinal regression problems, it is argued that the order relation on the classes should be reflected by the model structure as well as the performance measure used to evaluate the model. These arguments lead to a natural extension of the well-known proportional odds model for non-crisp ordinal regression problems, in which the underlying latent variable is not necessarily restricted to the class of linear models (by using kernel methods).