Introduction to the theory and applications of neural networks with quadratic junctions

The authors provide a statistical viewpoint for understanding and using a novel class of neural networks that contain quadratic junctions. It is shown that any Gaussian classifier can be mapped into a quadratic neuron. When the data cluster by means of hyperellipsoids, the quadratic neurons provide significant advantages over other representation schemes. Moreover, there are cases in which, even when the data are non-Gaussian, multilayer neural networks composed of quadratic neurons provide efficient solutions to these pattern recognition problems