On the quadratic extension of the canonical piecewise-linear network

The network on the canonical piecewise-linear representation (CPWL), compared to conventional mapping networks such as the backpropagation network and the radial basis network, has advantages in both learning, and implementation aspects. An extension of the CPWL network called the network of canonical piecewise-quadratic representation with linear partitions (CPWQ-L) is proposed. The CPWQ-L network shares the advantages of the CPWL network in explicitly and compactly realizing a spline approximation of nonlinear functions, while it extends the approximation capability of the latter at a low cost in computation and implementation. Examples of computer simulations are presented to demonstrate the superiority of the CPWQ-L network in some applications