Classification and dimensional reduction using restricted radial basis function networks

One of the most efficient means to understand complex data is by visualizing them in two- or three-dimensional space. As meaningful data are likely to be high dimensional, visualizing them requires dimensional reduction algorithms, which objective is to map high-dimensional data into low-dimensional space while preserving some of their underlying structures. For labeled data, their low-dimensional representations should embed their classifiability so that their class-structures become visible. It is also beneficial if an algorithm can classify labeled input while at the same time executes dimensional reduction to visually offer information regarding the data’s structure to give rational behind the classification. However, most of the currently available dimensional reduction methods are not usually equipped with classification features, while most classification algorithm lacks transparencies in rationalizing their decisions. In this paper, the restricted radial basis function networks (rRBF), a recently proposed supervised neural network with low-dimensional internal representation, is utilized for visualizing high-dimensional data while also performing classification. The primary focus of this paper is to empirically explain the classifiability and visual transparency of the rRBF.