An improved coordinate update method for the identification of adaptive hinging hyperplanes model

Adaptive hinging hyperplanes (AHH) is a popular continuous piecewise linear (CPWL) model. It has been proved that any continuous nonlinear function can be approximated by a CPWL function with arbitrary precision. The existing identification of AHH simply traverses all the dimensions on the pre-given splitting points to select the best, which fails to consider all the parameters synchronously and the randomness in the splitting, thus the identified model may not be optimal. In this paper, we propose an improved method to identify AHH model with coordinate update strategy. We first use the existing identification method of AHH to initially obtain a basic model structure, and afterwards alternatively optimize the parameters to improve accuracy. Specifically, to explore the interactive and global effects among all the nonlinear parameters, adaptive block coordinate DIRECT (ABCD) algorithm is employed to simultaneously optimize the nonlinear parameters, while the linear parameters can be calculated by least squares (LS) method. Besides, the proposed method is promising to conduct extensions to identify different CWPL models or other nonlinear models even with various error criteria. Numerical experiments show that the proposed method improves the accuracy and stability in identifying AHH and it can even achieve higher accuracy with simpler model structure.