A novel, geometric supervised learning scheme using linear programming approach

Based on a novel formulation of a two-layer, feedforward, artificial neural network that has hard-limited neuron response functions, the supervised learning problem of finding the connection matrix [a_ij] in terms of the required input-output mapping is viewed as an N-dimensional geometric problem. The solution of this geometric problem can be obtained by means of a generalized simplex method used in linear programming. Under a generalized feasibility criterion, [a_ij] is then solved uniquely. The method used is a one-step solve-all method instead of the conventional iterative, step-by-step method. The formulation and the solution of this geometric problem are discussed in detail, and numerical examples verifying the theoretical predictions are given