Learning in a single pass: a neural model for principal components analysis and linear regression

The authors describe a neural data-analyser. They first prove that the factors of principal components analysis (PCA)-i.e. the eigenvectors of the data covariance matrix-can be computed according to a recursive algorithm. They then derive a neural network extracting the factors of a vector data flow. This is achieved by a learning law, involving hebbian reinforcement and lateral interaction between neurons. A realistic implementation is then discussed. They also show how the former model can be used to implement learning gain control on a neural network achieving linear regression analysis. An important feature of the model is that it obtains the exact solutions to the problems of PCA and regression in a single learning pass on data patterns.