Vector Quantization by Neuro-Dynamical System

A new type of objective function is proposed for solving vector quantization problems by means of neural networks of Hopfield type. The extension of the domain of the function gives an energy function, by which a neuro-dynamical system is introduced. It is proved that any minimal point of the objective function is an equilibrium and asymptotically stable point of the system. Hence, the state of the system will approach to an optimal solution of the vector quantization problem when the initial state is set in the basin of a minimum point of the objective function.