Hebbian classification in and around the unit cube

A linear threshold unit is known to be capable of classifying multidimensional data, provided that the classes are linearly separable. Rosenblatt (1958) proposed a simple learning algorithm that, under linear separability, converges to a solution in a finite number of steps. The learning capacity of such a unit was shown by Cover (1965) to be twice the input dimension. A recently proposed model by the author (see Center for Intelligent Systems Report No. 9320, Technion, Israel Inst. of Technology, 1993), applying Rosenblatt´s learning rule to high-dimensional binary internal representations of the input vectors, was shown to remove both the low capacity and the linear separability limitations of the single cell. The learning time required by Rosenblatt´s learning may be reduced by applying the Hebbian learning rule to sparse binary internal representations calculated by a layer of spherical threshold cells. This applies to both binary and real-valued bounded input vectors. The activation radius of the internal cells is determined by the desired generalization capability and the minimal number of cells is determined by a requirement that the input space is covered with a sufficiently high probability. The learning capacity is twice the size of the internal layer. The performance of the basic classifier may be improved by laterally connecting the internal cells as in the corrective and the associative memory models proposed previously