Neural network approaches for the extraction of the eigenstructure

A feedback neural network for eigen-decomposition of a positive semidefinite matrix is presented. In the paper, we have shown the stability and real-time eigen-decomposition computation ability of the proposed neural network. The network can go into the stable state in the magnitude of the circuit time constant. The output voltage of the net, under the smallest energy state, is just the eigenvector corresponding to the minimum eigenvalue of the NN's connection strength matrix R, which is the direct use of the data covariance matrix without any pre-processing. By taking reasonable process to R, we can further extract the other eigen-parameters of R. A number of computer simulation results have been made to verify the effectiveness of the network. Both the theoretical analysis and the experimental results show that the proposed net can perform the extraction of the eigenstructure in real time.