A comprehensive understanding for radial basis probabilistic neural networks

The paper makes a profound analysis on radial basis probabilistic neural networks (RBPNN) from the viewpoint of linear algebra. Specifically, the transformation properties and internal representations of the RBPNNs are investigated in alliance with the properties of the input samples so that one may understand and grasp the mechanisms for pattern classification and function approximation of the RBPNNs. In addition, we analyse the convergence behaviour of the output class weight vectors of the RBPNNs, which can be shown to be orthogonal as well. Finally, one example for classifying five kinds of different distribution patterns are given to further support our understandings and claims.