N-tuple neural networks

The N-Tuple Neural Network (NTNN) is a fast, efficient memory-based neural network capable of performing non-linear function approximation and pattern classification. The random nature of the N-tuple sampling of the input vectors makes precise analysis difficult. Here, the NTNN is considered within a unifying framework of the General Memory Neural Network (GMNN) — a family of networks which include such important types as radial basis function networks. By discussing the NTNN within such a framework, a clearer understanding of its operation and efficient application can be gained. The nature of the intrinsic tuple distances, and the resultant kernel, is also discussed, together with techniques for handling non-binary input patterns. An example of a tuple-based network, which is a simple extension of the conventional NTNN, is shown to yield the best estimate of the underlying regression function, E(Y|x), for a finite training set. Finally, the pattern classification capabilities of the NTNN are considered.