Visualizing high dimensional data by projecting them into two or threedimensional space is one of the most effective ways to intuitively understandthe data's underlying characteristics, for example their class neighborhoodstructure. While data visualization in low dimensional space can be efficientfor revealing the data's underlying characteristics, classifying a new samplein the reduced-dimensional space is not always beneficial because of the lossof information in expressing the data. It is possible to classify the data inthe high dimensional space, while visualizing them in the low dimensionalspace, but in this case, the visualization is often meaningless because itfails to illustrate the underlying characteristics that are crucial for theclassification process. In this paper, the performance-preserving property of the previously proposedRestricted Radial Basis Function Network in reducing the dimension of labeleddata is explained. Here, it is argued through empirical experiments that theinternal representation of the Restricted Radial Basis Function Network, whichduring the supervised learning process organizes a visualizable two dimensionalmap, does not only preserve the topographical structure of high dimensionaldata but also captures their class neighborhood structures that are importantfor classifying them. Hence, unlike many of the existing dimension reductionmethods, the Restricted Radial Basis Function Network offers two dimensionalvisualization that is strongly correlated with the classification process.
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