  In the classical Gaussian SVM classification we use the feature space
projection transforming points to normal distributions with fixed covariance
matrices (identity in the standard RBF and the covariance of the whole dataset
in Mahalanobis RBF). In this paper we add additional information to Gaussian
SVM by considering local geometry-dependent feature space projection. We
emphasize that our approach is in fact an algorithm for a construction of the
new Gaussian-type kernel.
  We show that better (compared to standard RBF and Mahalanobis RBF)
classification results are obtained in the simple case when the space is
preliminary divided by k-means into two sets and points are represented as
normal distributions with a covariances calculated according to the dataset
partitioning.
  We call the constructed method C$_k$RBF, where $k$ stands for the amount of
clusters used in k-means. We show empirically on nine datasets from UCI
repository that C$_2$RBF increases the stability of the grid search (measured
as the probability of finding good parameters).
