Representing ordinal input variables in the context of ordinal classification

Ordinal input variables are common in many supervised and unsupervised machine learning problems. We focus on ordinal classification problems, where the target variable is also categorical and ordinal. In order to represent categorical input variables for measuring distances or applying continuous mapping functions, they have to be transformed to numeric values. This paper evaluates five different methods to do so. Two of them are commonly applied by practitioners, the first one based on binarising the ordinal input variable using standard indicator variables (NomBin), and the second one based on directly mapping each category to a consecutive natural number (Num). Furthermore, three novel proposals are evaluated in this paper: 1) an ordinal binarisation based on considering the order of the input variable (OrdBin), 2) the analysis of pairwise distances between input patterns to recover the latent variable generating the ordinal one (NumLVR), and 3) the refinement of the standard numeric transformation by recovering the distance between sets of patterns of consecutive categories (NumCDR). A thorough empirical evaluation is made, considering 12 datasets, 5 performance metrics and 4 classifiers (2 of them of nominal nature and 2 of ordinal nature). The results show that the Nom-Bin representation method leads to the worst results, and that both Num and NumCDR methods obtain very good performance, although NumCDR results are consistently better for almost all performance metrics and classifiers considered.