Semi-supervised Learning for Ordinal Kernel Discriminant Analysis

Ordinal classication considers those classication problems where the labels of the variable to predict follow a given order. Naturally, labelled data is scarce or di_cult to obtain in this type of problems because, in many cases, ordinal labels are given by an user or expert (e.g. in recommendation systems). Firstly, this paper develops a new strategy for ordinal classi_cation where both labelled and unlabelled data are used in the model construction step (a scheme which is referred to as semi-supervised learning). More specically, the ordinal version of kernel discriminant learning is extended for this setting considering the neighbourhood information of unlabelled data, which is proposed to be computed in the feature space induced by the kernel function. Secondly, a new method for semi-supervised kernel learning is devised in the context of ordinal classi_cation, which is combined with our developed classi_cation strategy to optimise the kernel parameters. The experiments conducted compare 6 different approaches for semi-supervised learning in the context of ordinal classication in a battery of 30 datasets, showing 1) the good synergy of the ordinal version of discriminant analysis and the use of unlabelled data and 2) the advantage of computing distances in the feature space induced by the kernel function.