Nonlinear principal component using feedforward neural network

An approach to unsupervised learning in a feedforward neural network is discussed. The linear feedforward neural network is similar to the principal component analysis, which is a linear reduction technique. Some nonlinear curvatures are embedded in the data set. This approach copes with both linear and nonlinear data patterns. The algorithm finds the nonlinear eigenvectors of the input correlation matrix R, Rx=λSx where S comes from the nonlinearity in the neural network. The problem is solved for finite-dimensional normed linear spaces using Brouwer´s fixed point theorem