特征结构提取的高阶Hopfield神经网络实现

本文首先建立了特征结构提取问题的罚函数表示，通过对罚函数求极小可以求得原始协方差矩阵的主特征向量及其对应的特征值。为了求得其他特征结构，特构造了一个协方差矩阵序列。如果将罚函数展开并进行整理，高阶Ｈｏｐｆｉｅｌｄ神经网络可被引入到特征结构提取中。这种方法比较直观，它将网络稳定时的输出与所求协方差矩阵的主特征向量的各个分量相对应，而网络稳定时的能量则对应于协方差矩阵的迹与所求特征值之差，计算机仿真结果验证了这种方法的正确性。

Implementation of the High-Order Hopfield Neural Networks for the Extraction of the Eigenstructures

The penalty function for the problem of the eigenstructure extraction is constructed.Through looking for the minimer of the penalty function,we can get the principal component of the original varance matrix.In order to get the other eigenstructures,a new variance matrix series is designed in the paper.If we spread out the penalty function and arrange it,the high-order Hopfield neural network can be introduced into the probglem.More directly,the method corresponds the outputs of the network when the network is stable to each of the princi-pal component of the corresponding matrix,and the energy of the stable network is equal to the difference between the trace of the covariance maxtrix and its principal eigenvalue.Computer simulation tests the method is reasonable.