Konstantin Emil Thiel

Density-based clustering aims to find groups of similar objects (i.e., clusters) in a given dataset. Applications include, e.g., process mining and anomaly detection. It comes with two user parameters (ε, MinPts) that determine the clustering result, but are typically unknown in advance. Thus, users need to interactively test various settings until satisfying clusterings are found. However, existing solutions suffer from the following limitations: (a) Ineffective pruning of expensive neighborhood computations. (b) Approximate clustering, where objects are falsely labeled noise. (c) Restricted parameter tuning that is limited to ε whereas MinPts is constant, which reduces the explorable clusterings. (d) Inflexibility in terms of applicable data types and distance functions. We propose FINEX, a linear-space index that overcomes these limitations. Our index provides exact clusterings and can be queried with either of the two parameters. FINEX avoids neighborhood computations where possible and reduces the complexities of the remaining computations by leveraging fundamental properties of density-based clusters. Hence, our solution is efficient and flexible regarding data types and distance functions. Moreover, FINEX respects the original and straightforward notion of density-based clustering. In our experiments on 12 large real-world datasets from various domains, FINEX frequently outperforms state-of-the-art techniques for exact clustering by orders of magnitude.

Ordinal data in a repeated measures design of a crossover study for rare diseases usually do not allow for the use of standard parametric methods, and hence, nonparametric methods should be considered instead. However, only limited simulation studies in settings with small sample sizes exist. Therefore, starting from an Epidermolysis Bullosa simplex trial with the above‐mentioned design, a rank‐based approach using the R package nparLD and different generalized pairwise comparisons (GPC) methods were compared impartially in a simulation study. The results revealed that there was not one single best method for this particular design, because a trade‐off exists between achieving high power, accounting for period effects, and for missing data. Specifically, nparLD as well as the unmatched GPC approaches do not address crossover aspects, and the univariate GPC variants partly ignore the longitudinal information. The matched GPC approaches, on the other hand, take the crossover effect into account in the sense of incorporating the within‐subject association. Overall, the prioritized unmatched GPC method achieved the highest power in the simulation scenarios, although this may be due to the specified prioritization. The rank‐based approach yielded good power even at a sample size of , whereas the matched GPC method could not control the type I error.