自适应链接超平面及其与高阶典范模型的比较

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

自适应链接超平面模型(AHH)是一种自适应的分片线性模型,可以作为一种人工神经网络用于非线性函数逼近。通过代数等价变换,该文证明,基于单纯形划分的高阶典范模型(HL-CPWL)的基函数等价于AHH模型的一种基函数,HL-CPWL模型是AHH模型的一个特例。较之HL-CPWL模型,AHH模型的定义域划分更为灵活,使得其更适合于函数逼近。AHH的通用逼近性也由HL-CPWL具有通用逼近能力而直接得到。仿真结果表明,较之HL-CPWL,AHH能够以较少的参数给出较好的逼近结果,具有更好的模型质量。

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.