An unsupervised learning rule for vector normalization and gain control

A neural network model is proposed for linear processing units and an unsupervised learning rule for normalizing input vectors drawn from a given probability distribution. After training the network, the gain with which the inputs are sampled is set at such a level that it yields a fixed mapping between the root of the average squared norm of the input vectors and the norm of the processing unit's outputs. Three cases of normalization are considered. The adaptive network simultaneously performs error correction and recalibration. It is shown that the author's learning rule solves the dual problem of Oja's single-unit unsupervised learning rule.<>