Artificial neural network for nonlinear projection of multivariate data

The authors propose a learning algorithm to train a multilayer feedforward neural network to perform the well-known Sammon nonlinear projection. The learning algorithm is an extension of the backpropagation algorithm. A significant advantage of the network-based projection over the original Sammon algorithm is that the trained network is able to project new patterns. Experimental results indicate that the projection network has good generalization capability when an appropriately sized training set and network are utilized. A lower bound for the number of free parameters required to achieve the same representation power as Shannon´s algorithm is derived. This lower bound, together with the generalization capability, provides some guidelines about the size of the network that should be used