An on-line learning algorithm using the decomposition and coordination of a neural network

A Neural network with a feed-forward structure with one input, one hidden and one output layer can be presented as a hierarchical two-level structure with two independent subnetworks on both the first and the second level. This process is known as decomposition of an Artificial Neural Network (ANN) into two sub-networks. Two target functions are defined: the output target function Ψ, which defines an error function for all networks. The local target function Φ which defines the error of the first and second layer sub-network adjustment. For the coordination level, two independent functions are defined: G(V) for feed forward and H(V) for back forward. The coordinator ensures that learning algorithms for both levels, first and second, are concatenated. Solving local tasks provides for the achievement of the minimum of the global target function Ψ (global task). The article defines the obligatory conditions that have to be fulfilled (regarding both the first and the second level tasks), for the algorithm to be convergent and achieve the minimum of the global target function (the output function). A three-argument function allows us to study the general learning characteristics for both the first and the second level. Final results are discussed and the positive and negative parameters of the two stage learning algorithm are presented. Matrix weight coefficients are modified after each presentation of learning vectors X (input) and Z (output).