Detecting Ordinal Subcascades

Ordinal classifier cascades are constrained by a hypothesised order of the semantic class labels of a dataset. This order determines the overall structure of the decision regions in feature space. Assuming the correct order on these class labels will allow a high generalisation performance, while an incorrect one will lead to diminished results. In this way ordinal classifier systems can facilitate explorative data analysis allowing to screen for potential candidate orders of the class labels. Previously, we have shown that screening is possible for total orders of all class labels. However, as datasets might comprise samples of ordinal as well as non-ordinal classes, the assumption of a total ordering might be not appropriate. An analysis of subsets of classes is required to detect such hidden ordinal substructures. In this work, we devise a novel screening procedure for exhaustive evaluations of all order permutations of all subsets of classes by bounding the number of enumerations we have to examine. Experiments with multi-class data from diverse applications revealed ordinal substructures that generate new and support known relations.