Hopfield Networks for Vector Quantization

We consider the problem of finding representative prototypes within a set of data and solve it using Hopfield networks. Our key idea is to minimize the mean discrepancy between kernel density estimates of the distributions of data points and prototypes. We show that this objective can be cast as a quadratic unconstrained binary optimization problem which is equivalent to a Hopfield energy minimization problem. This result is of current interest as it suggests that vector quantization can be accomplished via adiabatic quantum computing.