Adaptive Hinging Hyperplanes
نویسندگان
چکیده
The model of adaptive hinging hyperplanes (AHH) is proposed in this paper for black-box modeling. It is based on Multivariate Adaptive Regression Splines (MARS) and Generalized Hinging Hyperplanes (GHH) and shares attractive properties of the two. By making a modification to the basis function of MARS, AHH shows linear property in each subarea. It is proved that AHH model is identical to a special case of the Generalized Hinging Hyperplanes (GHH) model, which has a universal representation capability for continuous piecewise linear functions. AHH algorithm is developed similar to MARS algorithm. It is adaptive and can be executed quickly, hence has power and flexibility to model unknown relationships. In addition, due to the piecewise-linear property, AHH is preferred to MARS when modeling high-dimensional dynamic systems, especially when the sample size is small and under noise conditions.
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