特征向量计算的神经网络方法

NEURON COMPUTATION METHODS ON CALCULATING EIGENVECTORS

矩阵特征向量计算在实际问题中有着广泛应用．本文采用神经网络计算方法来研究主元分析（ＰＣＡ）和次元分析（ＭＣＡ）问题．我们首先考虑单神经元的情况（ｐ＝１），给出了求矩阵最大特征元和最小特征元的算法．然后对多神经元情形（ｐ＞１），给出了抽取矩阵主元和次元的算法．和目前许多已知的算法不一样，在我们ＰＣＡ的算法中改变矩阵的负号就能够得到ＭＣＡ问题的解．

In practical life, how to compute eigenvectors has much application. In this paper, by using the method of neuron computation, problems on the principle component analysis (PCA) and on the minor component analysis are studied. First, for the single neutron case p = 1, algorithms on computing the principle component and the minor component of a matrix are presented. Secondly, for the several neutrons case p > 1, algorithms on computing several principle components and several minor components of a matrix are obtained. Our algorithms on MCA can be immediately deduced from our algorithms on PAC by changing the sign, which is different from most conventional algorithms.