用于非高斯系统降维的最小残差熵主元网络

基于最小均方误差的主元分析和主元神经网络是有效的多变量降维统计技术,它们所提取的主元含有系统最大方差.非高斯随机系统的近似模型应当含有系统最大信息熵,但包含最大方差并不一定包含最大信息熵.该文提出一种以最小残差熵为通用指标的非线性主元神经网络模型,并给出了一种基于Parzen窗口密度函数估计的熵近似计算方法和网络学习算法.然后从信息论角度分析了,在高斯随机系统中基于最小残差熵和最小均方差为指标的主元网络学习结果具有一致性.最后以仿真验证该方法的有效性,并与基于最小均方误差的主元分析和主元神经网络方法的计算结果进行对比性分析.

A Principal Component Neural Network with Minimum Error Entropy for Dimension Reduction of Non-Gaussian System

The principal component analysis(PCA) and the principal component neural networks(PCNNs) based on the criteria of the least mean squared errors(MSEs) are effective approaches of dimension reduction for Gaussian system data.But for non-Gaussian stochastic system PCNNs with minimum reconstruction squared error do not contain maximum information about original system definitely.The error entropy criterion imposes the minimization of average information content in the error signal rather than simply minimizing the energy as MSE does.In this paper,a PCNN model with minimum error entropy is introduced firstly.And then an approximation method of Shannon entropy with a Parzen density estimator and the corresponding learning algorithm are proposed.Finally the simulation results with the indices of least mean squared errors and minimum error entropy are compared and the encouraging results have been obtained.