Identification algorithm for standard continuous piecewise linear neural network

Standard continuous piecewise linear neural network (SCPLNN) is a new continuous piecewise linear (CPL) model. It can represent all the CPL functions and approximate any continuous nonlinear function with arbitrary precision. Moreover, the parameters of SCPLNN are directly related to the expression of the subregions, in each of which SCPLNN equals to a linear function. Based on this property, this paper proposes an identification algorithm for SCPLNN, including domain partition and parameters optimization. In numerical experiments, SCPLNN with this algorithm outperforms hinging hyperplanes which is a widely used CPL model, showing the power and flexibility of SCPLNN in approximation.