基于RBF神经网络的非线性主元分析新方法

在分析非线性主元曲线性质基础上,提出了非线性负载是变量X的函数,基于此,设计非线性负载RBF神经网络结构,给出了随机梯度下降算法。提出的非线性主成分分析方法与以往方法比较,得分和负载在概念上具有和线性主成分分析相同的解释,在结构上较为简单,解决了缺乏训练数据问题,训练容易。与线性主成分分析的对比仿真验证了提出方法的有效性。

New Nonlinear Principal Analysis Method Based on RBF Neural Network

Based on the analysis of non-linear principal component curve,it was proposed that non-linear projecting direction(PD) was the function of variable X. Accordingly,an RBF neural network structure was designed and a stochastic gradient descent algorithm was given to seek PD. Compared with other methods,scores and loadings of the nonlinear principal component analysis(NLPCA) method have the same interpretations as linear Principal Component Analysis(PCA). It is easy to train the NN with simpler structure. Moreover,the method gets over the difficulty of lacking training data. Simulation results show that the proposed method is more effective compared with linear PCA.