Ordinal classification: working definition and detection of ordinal structures

Ordinal classification (OC) is an important niche of supervised pattern recognition, in which the classes constitute an ordinal structure. In general, the ordinal structure can be identified, either according to the natural occurrence of the current task (e.g. healthy - mild condition - moderate condition - severe condition), or by extracting expert knowledge. However, we assume that many multi-class classification tasks might have a hidden ordinal structure, which, once identified, can facilitate and hence leverage the classification process. Therefore, we propose a working definition for OC tasks, which is based on the decision boundaries of standard binary Support Vector Machines. Moreover, resulting from our proposed definition, we introduce a simple algorithm for the detection of ordinal structures. Our proposed definition is easy to interpret and reflects an intuitive understanding of ordinal structures. Another main advantage is that our proposed definition is easy to apply. Therefore, there is no more dependence on expert knowledge for the identification of (non-intuitive) ordinal class structures. In the current study, we include ten benchmark data sets from the field of OC to experimentally evaluate and hence to confirm the validity of our proposed definition. Additionally, we analyse our proposed definition based on a small set of traditionally non-ordinal multi-class classification tasks. Furthermore, we provide an analysis of the computational cost of our proposed detection algorithm, and discuss the limitations of our proposed working definition