Generalized inverse computations using two-layer feedforward neural networks with pruning

We study the computations of generalized inverses (GI´s) of a matrix using two-layer feedforward neural networks (TFNN), which provides an alternative to the traditional methods based on matrix decompositions. The required GI solution of a given matrix is obtained from outputs of the converged networks while the minimum point of a cost function reveals useful rank information about the matrix. The stability and convergence of the back-propagation (BP) learning algorithm is shown to be closely related to the spread of nonzero singular values of some underlying matrix. Also by identifying the relation, between the optimal number of hidden nodes of the TFNN and the matrix rank, we are able to prune the network by removing those redundant hidden nodes so that an optimal network structure is produced upon the convergence of learning. Simulation results are presented to confirm the analysis