  Visualizing high dimensional data by projecting them into two or three
dimensional space is one of the most effective ways to intuitively understand
the data's underlying characteristics, for example their class neighborhood
structure. While data visualization in low dimensional space can be efficient
for revealing the data's underlying characteristics, classifying a new sample
in the reduced-dimensional space is not always beneficial because of the loss
of information in expressing the data. It is possible to classify the data in
the high dimensional space, while visualizing them in the low dimensional
space, but in this case, the visualization is often meaningless because it
fails to illustrate the underlying characteristics that are crucial for the
classification process.
  In this paper, the performance-preserving property of the previously proposed
Restricted Radial Basis Function Network in reducing the dimension of labeled
data is explained. Here, it is argued through empirical experiments that the
internal representation of the Restricted Radial Basis Function Network, which
during the supervised learning process organizes a visualizable two dimensional
map, does not only preserve the topographical structure of high dimensional
data but also captures their class neighborhood structures that are important
for classifying them. Hence, unlike many of the existing dimension reduction
methods, the Restricted Radial Basis Function Network offers two dimensional
visualization that is strongly correlated with the classification process.
