算法的迭代步长对于算法的收敛性能有着重要影响.针对固定步长的非线性主成分分析(NPCA)算法不能兼顾收敛速度和估计精度的情形,提出基于梯度的自适应变步长NPCA算法和最优变步长NPCA算法两种自适应变步长算法来改善其收敛性能.特别地,最优变步长NPCA算法通过对代价函数进行一阶线性近似表示,从而计算出当前的最优迭代步长.该算法的迭代步长随估计误差的变化而变化,估计误差大,迭代步长相应大,反之亦然；且不需要人工设置任何参数.仿真结果表明,当算法的估计精度相同时,与固定步长NPCA算法相比,两种自适应变步长NPCA算法相对固定步长NPCA算法都具有更好的收敛速度或跟踪性能,且最优变步长NPCA算法的性能优于基于梯度的自适应变步长NPCA算法.%The design of the step-size is crucial to the convergence rate of the Nonlinear Principle Component Analysis (NPCA) algorithm. However, the commonly used fixed step-size algorithm can hardly satisfy the convergence speed and estimation precision requirements simultaneously. To address this issue, the gradient-based adaptive step-size NPCA algorithm and optimal step-size NPCA algorithm were proposed to speed up the convergence rate and improve tracking ability. In particular, the optimal step-size NPCA algorithm linearly approximated the contrast function and figured out the optimal step-size currently. The optimal step-size NPCA algorithm utilized an adaptive step-size whose value was adjusted in sympathy with the value of the contrast function and free from any manual parameters. The simulation results show that the proposed adaptive step-size NPCA algorithms have faster convergence rate or better tracking ability in comparison with the fixed step-size NPCA algorithm when the estimation precisions are same. The convergence performance of the optimal step-size NPCA algorithm is superior to that of the gradient-based adaptive NPCA algorithm.
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