Skip to Main Content
A condition for separation of two categories by a pattern-recognition network formed by an array of threshold logic units (TLU) and an additional decision element is discussed. The array implements a set of hyperplanes that partition the sample space, and the array outputs and the sample vector elements form the input to the decision element. It is shown that this input is separable by a convex surface if, in each of the cells in the partition, the convex hull of the first-category vectors in that cell does not intersect with the convex hull of the second-category vectors in that cell. When the TLU outputs can be set to zero by another TLU in the array, a comparison shows that the network capacity can be significantly increased. A sufficient condition for the array outputs to be in general position is described. An algorithm is suggested that places the hyperplanes so that equal error rates occur on both sides. This property tends to more finely partition regions with overlap between categories.