@article{LausserSchaeferWerleetal.2020, author = {Lausser, Ludwig and Sch{\"a}fer, Lisa M. and Werle, Silke D. and Kestler, Angelika M. R. and Kestler, Hans A.}, title = {Detecting Ordinal Subcascades}, volume = {52}, journal = {Neural Processing Letters}, number = {3}, publisher = {Springer Science+Business Media}, address = {Dordrecht}, issn = {1573-773X}, doi = {https://doi.org/10.1007/s11063-020-10362-0}, pages = {2583 -- 2605}, year = {2020}, abstract = {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.}, language = {en} } @article{LausserSchaeferKestler2018, author = {Lausser, Ludwig and Sch{\"a}fer, Lisa M. and Kestler, Hans A.}, title = {Ordinal Classifiers Can Fail on Repetitive Class Structures}, volume = {4 (2018)}, journal = {Archives of Data Science, Series A}, number = {1}, publisher = {KIT Scientific Publishing}, address = {Karlsruhe}, issn = {2363-9881}, doi = {https://doi.org/10.5445/KSP/1000085951/25}, year = {2018}, abstract = {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.}, language = {en} } @article{LausserSchaeferSchirraetal.2019, author = {Lausser, Ludwig and Sch{\"a}fer, Lisa M. and Schirra, Lyn-Rouven and Szekely, Robin and Schmid, Florian and Kestler, Hans A.}, title = {Assessing phenotype order in molecular data}, volume = {9}, pages = {11746}, journal = {Scientific Reports}, publisher = {Springer Nature}, address = {London}, issn = {2045-2322}, doi = {https://doi.org/10.1038/s41598-019-48150-z}, year = {2019}, abstract = {Biological entities are key elements of biomedical research. Their definition and their relationships are important in areas such as phylogenetic reconstruction, developmental processes or tumor evolution. Hypotheses about relationships like phenotype order are often postulated based on prior knowledge or belief. Evidence on a molecular level is typically unknown and whether total orders are reflected in the molecular measurements is unclear or not assessed. In this work we propose a method that allows a fast and exhaustive screening for total orders in large datasets. We utilise ordinal classifier cascades to identify discriminable molecular representations of the phenotypes. These classifiers are constrained by an order hypothesis and are highly sensitive to incorrect assumptions. Two new error bounds, which are introduced and theoretically proven, lead to a substantial speed-up and allow the application to large collections of many phenotypes. In our experiments we show that by exhaustively evaluating all possible candidate orders, we are able to identify phenotype orders that best coincide with the high-dimensional molecular profiles.}, language = {en} }