Kernelising the Proportional Odds Model through kernel learning techniques

Abstract

The classification of patterns into naturally ordered labels is referred to as ordinal regression, which is a very common setting for real world applications. One of the most widely used ordinal regression algorithms is the Proportional Odds Model (POM), despite the linearity of the resultant decision boundaries. Through different proposals, this paper explores the notions of kernel trick and empirical feature space to reformulate the POM method and obtain nonlinear decision boundaries. Moreover, a new technique for aligning the kernel matrix taking into account the ordinal problem information is proposed, as well as a regularised gradient ascent methodology which is used to select the optimal dimensionality for the empirical feature space. The capability of the different developed methodologies is evaluated by the use of a nonlinearly separable toy dataset and an extensive set of experiments over 28 ordinal datasets. The results indicate that the tested methodologies are competitive with respect to other state-of-the-art algorithms, and they significantly improve the original POM algorithm.