Inconsistency in prediction problems occurs when instances that relate in a certain way on condition attributes, do not follow the same relation on the decision attribute. For example, in ordinal classification with monotonicity constraints, it occurs when an instance dominating another instance on condition attributes has been assigned to a worse decision class. It typically appears as a result of perturbation in data caused by incomplete knowledge (missing attributes) or by random effects that occur during data generation (instability in the assessment of decision attribute values). Inconsistencies with respect to a crisp preorder relation (expressing either dominance or indiscernibility between instances) can be handled using symbolic approaches like rough set theory and by using statistical/machine learning approaches that involve optimization methods. Fuzzy rough sets can also be seen as a symbolic approach to inconsistency handling with respect to a fuzzy relation. In this article, we introduce a new machine learning method for inconsistency handling with respect to a fuzzy preorder relation. The novel approach is motivated by the existing machine learning approach used for crisp relations. We provide statistical foundations for it and develop optimization procedures that can be used to eliminate inconsistencies. The article also proves important properties and contains didactic examples of those procedures.

We provide a thorough treatment of hyperparameter optimisation for three data descriptors with a good track-record in the literature: Support Vector Machine (SVM), Nearest Neighbour Distance (NND) and Average Localised Proximity (ALP). The hyperparameters of SVM have to be optimised through cross-validation, while NND and ALP allow the reuse of a single nearest-neighbour query and an efficient form of leave-one-out validation. We experimentally evaluate the effect of hyperparameter optimisation with 246 classification problems drawn from 50 datasets. From a selection of optimisation algorithms, the recent Malherbe-Powell proposal optimises the hyperparameters of all three data descriptors most efficiently. We calculate the increase in test AUROC and the amount of overfitting as a function of the number of hyperparameter evaluations. After 50 evaluations, ALP and SVM both significantly outperform NND. The performance of ALP and SVM is comparable, but ALP can be optimised more efficiently, while a choice between ALP and SVM based on validation AUROC gives the best overall result. This distils the many variables of one-class classification with hyperparameter optimisation down to a clear choice with a known trade-off, allowing practitioners to make informed decisions.

One-class classification is a challenging subfield of machine learning in which so-called data descriptors are used to predict membership of a class based solely on positive examples of that class, and no counter-examples. A number of data descriptors that have been shown to perform well in previous studies of one-class classification, like the Support Vector Machine (SVM), require setting one or more hyperparameters. There has been no systematic attempt to date to determine optimal default values for these hyperparameters, which limits their ease of use, especially in comparison with hyperparameter-free proposals like the Isolation Forest (IF). We address this issue by determining optimal default hyperparameter values across a collection of 246 one-class classification problems derived from 50 different real-world datasets. In addition, we propose a new data descriptor, Average Localised Proximity (ALP) to address certain issues with existing approaches based on nearest neighbour distances. Finally, we evaluate classification performance using a leave-one-dataset-out procedure, and find strong evidence that ALP outperforms IF and a number of other data descriptors, as well as weak evidence that it outperforms SVM, making ALP a good default choice.