Ordinal Classifiers Can Fail on Repetitive Class Structures

Ordinal classifiers are constrained classification algorithms that assume a predefined (total) order of the class labels to be reflected in the feature space of a dataset. This information is used to guide the training of ordinal classifiers and might lead to an improved classification performance. Incorrect assumptions on the order of a dataset can result in diminished detection rates. Ordinal classifiers can, therefore, be used to screen for ordinal class structures within a feature representation. While it was shown that algorithms could in principle reject incorrect class orderings, it is unclear if all remaining candidate orders reflect real ordinal structures in feature space. In this work we characterize the decision regions induced by ordinal classifiers. We show that they can fulfill different criteria that might be considered as ordinal reflections. These criteria are mainly determined by the connectedness and the neighborhood of the decision regions. We evaluate them for ordinal classifier cascades constructed from binary classifiers. We show that depending on the type of base classifier they bear the risk of not rejecting non ordinal, like partial repetitive, structures.