Adaptive hinging hyperplane and its comparison with high-level canonical piecewise linear representation

The model of adaptive hinging hyperplanes (AHH) is a continuous piecewise linear model and can be used as a neural network in nonlinear approximation. Through algebraic transformation, this paper proves that the basis function of a high-level canonical piecewise linear model (HL-CPWL) is equivalent to one kind of the AHH basis, thus the HL-CPWL model is actually a special AHH model. The domain partition introduced by the AHH model is more general than the simplicial partition in the HL-CPWL case, making AHH model more powerful in nonlinear function approximation. The universal approximation ability of AHH is naturally followed as HL-CPWL possesses the same ability. Simulations show that the AHH model gives a better approximation results with much fewer parameters, indicating that AHH is superior to HL-CPWL when the model quality is concerned about.