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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。
In this paper, we first establish the penalty function representation of the feature extraction problem, and obtain the main eigenvectors of the original covariance matrix and its corresponding eigenvalues by minimizing the penalty function. In order to find other features, we constructed a covariance matrix sequence. If the penalty function is expanded and collated, higher order Hopfield neural networks can be introduced into the feature extraction. This method is straightforward. It corresponds the output of the network with the components of the main eigenvector of the covariance matrix, while the energy of the network stability corresponds to the difference between the trace of the covariance matrix and the eigenvalue Computer simulation results verify the correctness of this method.