  For numerous reasons there raises a need for dimension reduction that
preserves certain characteristics of data. In this work we focus on data coming
from a mixture of Gaussian distributions and we propose a method that preserves
distinctness of clustering structure, although the structure is assumed to be
yet unknown. The rationale behind the method is the following: (i) had one
known the clusters (classes) within the data, one could facilitate further
analysis and reduce space dimension by projecting the data to the Fisher's
linear subspace, which -- by definition -- preserves the structure of the given
classes best (ii) under some reasonable assumptions, this can be done, albeit
approximately, without the prior knowledge of the clusters (classes). In the
paper, we show how this approach works. We present a method of preliminary data
transformation that brings the directions of largest overall variability close
to the directions of the best between-class separation. Hence, for the
transformed data, simple PCA provides an approximation to the Fisher's
subspace. We show that the transformation preserves distinctness of unknown
structure in the data to a great extent.
