A neural network with Boolean output layer

The design of feed-forward adaptive linear neuron (ADALINE) neural networks can be split into two: (1) designing the first hidden layer which uses linear hyperplanes to partition the continuous amplitude input space into a number of cells, and (2) designing the second and succeeding hidden layers which group the cells to larger decision regions. The design of the first hidden layer and of the Boolean output layer are discussed. The first procedure is basically a vector quantization of the pattern space that linearly separates all training patterns. Each cell in the vector quantization lattice is completely determined by a code address which is generated by the first hidden layer when only a pattern of the training set is supplied to the input of the neural network. The second problem is then to form a closed decision region as a Boolean function of cell addresses. A procedure is devised that minimizes this Boolean function by incorporation of free cells in the lattice, cells that are not addressed by the training patterns. It is shown that the second and succeeding hidden layers in a feed-forward network may therefore be replaced by a simple logical network. An algorithm for the design of this logical network is devised