  The problem of inhomogeneous cluster densities has been a long-standing issue
for distance-based and density-based algorithms in clustering and anomaly
detection. These algorithms implicitly assume that all clusters have
approximately the same density. As a result, they often exhibit a bias towards
dense clusters in the presence of sparse clusters. Many remedies have been
suggested; yet, we show that they are partial solutions which do not address
the issue satisfactorily. To match the implicit assumption, we propose to
transform a given dataset such that the transformed clusters have approximately
the same density while all regions of locally low density become globally low
density -- homogenising cluster density while preserving the cluster structure
of the dataset. We show that this can be achieved by using a new
multi-dimensional Cumulative Distribution Function in a transform-and-shift
method. The method can be applied to every dataset, before the dataset is used
in many existing algorithms to match their implicit assumption without
algorithmic modification. We show that the proposed method performs better than
existing remedies.
