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