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.