Generalization ability of optimal cluster separation networks

Optimal separation of two clusters of normalized vectors can be performed in a neural network with adjustable threshold and weights, which is trained to maximum stability. Generalization from arbitrarily selected training clusters to a given bipartitioning of input space is studied. The network's threshold becomes a global optimization (and order) parameter, This causes the generalization ability to increase rapidly with the distance of the cluster separation plane from the origin. Separation is shown to be stochastic for small and deterministic for large training cluster sizes.