Magnification control for batch neural gas

It is well known, that online neural gas (NG) possesses a magnification exponent different from the information theoretically optimum one in adaptive map formation. The exponent can explicitely be controlled by a small change of the learning algorithm. Batch NG constitutes a fast alternative optimization scheme for NG vector quantizers which possesses the same magnification factor as standard online NG. In this paper, we propose a method to integrate magnification control by local learning into batch NG by linking magnification control to an underlying cost function. We validate the learning rule in an experimental setting.