Classification of Ordinal Data

Predictive learning has traditionally been a standard indu ctive learning, where different sub-problem formulations have been identified. One of the most re presentative is classification, consisting on the estimation of a mapping from the feature sp ace into a finite class space. Depending on the cardinality of the finite class space we are l eft with binary or multiclass classification problems. Finally, the presence or absence o r a "natural" order among classes will separate nominal from ordinal problems. Although two-class and nominal classification problems hav e been dissected in the literature, the ordinal sibling has not yet received a lot of attention, e ven with many learning problems involving classifying examples into classes which have a na tural order. Scenarios in which it is natural to rank instances occur in many fields, such as info rmation retrieval, collaborative filtering, econometric modeling and natural sciences. Conventional methods for nominal classes or for regression problems could be employed to solve ordinal data problems; however, the use of techniques designed specifically for ordered classes yields simpler classifiers, making it easier to inte rpret the factors that are being used to discriminate among classes, and generalises better. Alt hough the ordinal formulation seems conceptually simpler than nominal, some technical di fficulties to incorporate in the algorithms this piece of additional information - the order - may explain the widespread use of conventional methods to tackle the ordinal data problem. This dissertation addresses this void by proposing a nonpar ametric procedure for the classification of ordinal data based on the extension of the original dataset with additional variables, reducing the classification task to the well-known two-clas s problem.