Non-linear principal components: projection and reconstruction

We review a negative feedback implementation of a Principal Component Analysis artificial neural network and show how, by decoupling the feedforward and feedback mechanism, we may separately affect the projection and reconstruction stages of the network. We therefore introduce a nonlinearity into the projection stage and compare the resulting mapping with a mixture of linear principal components. Finally we derive learning rules which are more optimal for different types of noise and illustrate the resulting network´s greater stability on an artificial data set corrupted by shot noise.