Derivation of a class of training algorithms

A novel derivation is presented of T. Kohonen´s topographic mapping training algorithm (Self-Organization and Associative Memory, 1984), based upon an extension of the Linde-Buzo-Gray (LBG) algorithm for vector quantizer design. Thus a vector quantizer is designed by minimizing an L₂ reconstruction distortion measure, including an additional contribution from the effect of code noise which corrupts the output of the vector quantizer. The neighborhood updating scheme of Kohonen´s topographic mapping training algorithm emerges as a special case of this code noise model. This formulation of Kohonen´s algorithm is a specific instance of the robust hidden layer principle, which stabilizes the internal representations chosen by a network against anticipated noise or distortion processes