A HIGHER-ORDER HOPFIELD NETWORK FOR VECTOR QUANTIZATION

A higher order version of the Hopfield neural network is presented whi ch will perform a simple vector quantisation or clustering function. T his model requires no penalty terms to impose constraints in the Hopfi eld energy, in contrast to the usual one where the energy involves onl y terms quadratic in the state vector The energy function is shown to have no local minima within the unit hypercube of the state vector so the network only converges to valid final states. Optimisation trials show that the network can consistently find optimal clusterings for sm all, trial problems and near optimal ones for a large data set consist ing of the intensity values from a digitised, grey-level image.