We propose polar encoding, a representation of categorical and numerical $[0,1]$-valued attributes with missing values to be used in a classification context. We argue that this is a good baseline approach, because it can be used with any classification algorithm, preserves missingness information, is very simple to apply and offers good performance. In particular, unlike the existing missing-indicator approach, it does not require imputation, ensures that missing values are equidistant from non-missing values, and lets decision tree algorithms choose how to split missing values, thereby providing a practical realisation of the "missingness incorporated in attributes" (MIA) proposal. Furthermore, we show that categorical and $[0,1]$-valued attributes can be viewed as special cases of a single attribute type, corresponding to the classical concept of barycentric coordinates, and that this offers a natural interpretation of polar encoding as a fuzzified form of one-hot encoding. With an experiment based on twenty real-life datasets with missing values, we show that, in terms of the resulting classification performance, polar encoding performs better than the state-of-the-art strategies \e{multiple imputation by chained equations} (MICE) and \e{multiple imputation with denoising autoencoders} (MIDAS) and -- depending on the classifier -- about as well or better than mean/mode imputation with missing-indicators.

We present the first comprehensive and large-scale evaluation of classical (NN), fuzzy (FNN) and fuzzy rough (FRNN) nearest neighbour classification. We show that existing proposals for nearest neighbour weighting can be standardised in the form of kernel functions, applied to the distance values and/or ranks of the nearest neighbours of a test instance. Furthermore, we identify three commonly used distance functions and four scaling measures. We systematically evaluate these choices on a collection of 85 real-life classification datasets. We find that NN, FNN and FRNN all perform best with Boscovich distance. NN and FRNN perform best with a combination of Samworth rank- and distance weights and scaling by the mean absolute deviation around the median ($r_1$), the standard deviaton ($r_2$) or the interquartile range ($r_{\infty}^*$), while FNN performs best with only Samworth distance-weights and $r_1$- or $r_2$-scaling. We also introduce a new kernel based on fuzzy Yager negation, and show that NN achieves comparable performance with Yager distance-weights, which are simpler to implement than a combination of Samworth distance- and rank-weights. Finally, we demonstrate that FRNN generally outperforms NN, which in turns performs systematically better than FNN.

Angular Minkowski $p$-distance is a dissimilarity measure that is obtained by replacing Euclidean distance in the definition of cosine dissimilarity with other Minkowski $p$-distances. Cosine dissimilarity is frequently used with datasets containing token frequencies, and angular Minkowski $p$-distance may potentially be an even better choice for certain tasks. In a case study based on the 20-newsgroups dataset, we evaluate clasification performance for classical weighted nearest neighbours, as well as fuzzy rough nearest neighbours. In addition, we analyse the relationship between the hyperparameter $p$, the dimensionality $m$ of the dataset, the number of neighbours $k$, the choice of weights and the choice of classifier. We conclude that it is possible to obtain substantially higher classification performance with angular Minkowski $p$-distance with suitable values for $p$ than with classical cosine dissimilarity.

Fuzzy rough set theory can be used as a tool for dealing with inconsistent data when there is a gradual notion of indiscernibility between objects. It does this by providing lower and upper approximations of concepts. In classical fuzzy rough sets, the lower and upper approximations are determined using the minimum and maximum operators, respectively. This is undesirable for machine learning applications, since it makes these approximations sensitive to outlying samples. To mitigate this problem, ordered weighted average (OWA) based fuzzy rough sets were introduced. In this paper, we show how the OWA-based approach can be interpreted intuitively in terms of vague quantification, and then generalize it to Choquet-based fuzzy rough sets (CFRS). This generalization maintains desirable theoretical properties, such as duality and monotonicity. Furthermore, it provides more flexibility for machine learning applications. In particular, we show that it enables the seamless integration of outlier detection algorithms, to enhance the robustness of machine learning algorithms based on fuzzy rough sets.

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.