Time series prediction for economic processes is a topic of increasing interest. In order to reduce stock-keeping costs, a proper forecast of the demand in the future is necessary. In this paper we use artificial neural networks for a short term forecast for the sale of articles in supermarkets. The nets are trained on the known sales volume of the past for a certain group of related products. In addition information like changing prices and advertising campaigns is also given to the net to improve the prediction quality. The net is trained on a window of inputs describing a fixed set of recent past states by the back-propagation algorithm [1].
For enhancement the algorithm has been parallelized in different manners: First the training set can be partitioned for the batch learning implementation. The neural network is duplicated on every processor of the parallel machine, and each processor works with a subset of the training set. After each epoch of training the weight changes are broadcasted and merged.
The second way is the parallel calculation of the matrix products that are used in the learning algorithm. The neurons in each layer are partitioned into p disjoint sets and each set is mapped on one of the p processors. The new activations are distributed after each training pair. We have implemented this on-line training in two variants: For the first parallelization one matrix product is not determined on one processor, but it is calculated while the partial sums are sent around on a processor cycle. The second method tries to reduce communication time. Therefor it needs an overhead in both storage and number of computational operations.
The parallel implementations take place on parallel Transputer-based PARSYTEC systems: a GCel with T805 and a GC/PP with PowerPC processors and Transputer communication links. The parallelizations run with both the runtime envirionments PARIX and PVM.