  Although distance measures are used in many machine learning algorithms, the
literature on the context-independent selection and evaluation of distance
measures is limited in the sense that prior knowledge is used. In cluster
analysis, current studies evaluate the choice of distance measure after
applying unsupervised methods based on error probabilities, implicitly setting
the goal of reproducing predefined partitions in data. Such studies use
clusters of data that are often based on the context of the data as well as the
custom goal of the specific study. Depending on the data context, different
properties for distance distributions are judged to be relevant for appropriate
distance selection. However, if cluster analysis is based on the task of
finding similar partitions of data, then the intrapartition distances should be
smaller than the interpartition distances. By systematically investigating this
specification using distribution analysis through a mirrored-density plot, it
is shown that multimodal distance distributions are preferable in cluster
analysis. As a consequence, it is advantageous to model distance distributions
with Gaussian mixtures prior to the evaluation phase of unsupervised methods.
Experiments are performed on several artificial datasets and natural datasets
for the task of clustering.
