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There are many distance-based methods for classification and clustering, andfor data with a high number of dimensions and a lower number of observations,processing distances is computationally advantageous compared to the raw datamatrix. Euclidean distances are used as a default for continuous multivariatedata, but there are alternatives. Here the so-called Minkowski distances, $L_1$(city block)-, $L_2$ (Euclidean)-, $L_3$-, $L_4$-, and maximum distances arecombined with different schemes of standardisation of the variables beforeaggregating them. Boxplot transformation is proposed, a new transformationmethod for a single variable that standardises the majority of observations butbrings outliers closer to the main bulk of the data. Distances are compared insimulations for clustering by partitioning around medoids, complete and averagelinkage, and classification by nearest neighbours, of data with a low number ofobservations but high dimensionality. The $L_1$-distance and the boxplottransformation show good results.

Minkowski distances and standardisation for clustering and classification of high dimensional data