The bridge relating process neural networks and traditional neural networks

The process neural network (PrNN) is an ANN model suited for solving the learning problems with signal inputs, whose elementary unit is the process neuron (PN), an emerging neuron model. There is an essential difference between the process neuron and traditional neurons, but there also exists a relation between them. The former can be approximated by the latter within any precision. First, the PN model and some PrNNs are introduced in brief. And then, two PN approximating theorems are presented and proved in detail. Each theorem gives an approximating model to the PN model, i.e., the time-domain feature expansion model and the orthogonal decomposition feature expansion model. Some corollaries are given for the PrNNs based on these two theorems. Thereafter, simulation studies are performed on some simulated signal sets and a real dataset. The results show that the PrNN can effectively suppress noises polluting the signals and generalize quite well. Finally some problems on PrNNs are discussed and further research directions are suggested.