On the design principles of the functional link nets

A necessary and sufficient condition for the nonexistence of a local stationary point for functional link nets is derived. The condition reveals the dependency of training errors on the rank of training samples and functional links and provides a guideline for selection of the functional links as well as training samples. An analytical solution is characterized, showing that the training task in the functional link nets can be reduced to solving a set of linear equations. A learning algorithm based on the recursive-least squares estimation method is proposed. Numerical examples are presented to substantiate the theoretical arguments