Asynchronous self-organizing maps

A recently defined energy function which leads to a self-organizing map is used as a foundation for an asynchronous neural-network algorithm. We generalize the existing stochastic gradient approach to an asynchronous parallel stochastic gradient method for generating a topological map on a distributed computer system (MIMD). A convergence proof is presented and simulation results on a set of problems are included. A practical problem using the energy function approach is that a summation over the entire network is required during the computation of updates. Using simulations we demonstrate effective algorithms that use efficient sampling for the approximation of these sums.