Orthogonal functional basis neural network for functional approximation

Subset selection is a well-known technique for generating an efficient and effective neural network structure. The technique has been combined with regularization to improve the generalization performance of a neural network. In this paper, we show an incongruity involving subset selection and regularization. We present an approach to solve this dissonance wherein our subset selection is derived from a combination of functional basis. A more efficient training convergence speed is shown using the new basis which is derived from an `orthogonal-functional-basis´ transformation. With this transformation we propose a new orthogonal functional basis neural network structure which is not only more computationally tractable but also gives better generalization performance. Simulation studies are presented that demonstrate the performance, behavior, and advantages of the proposed network