A class of nonlinear recognition procedures

In statistical recognition, the functional form of the underlying probability distributions determines the structure of recognition networks. Two approaches toward deriving a hierarchy of recognition procedures are reviewed and their implications concerning realization and estimation of recognition weights are discussed. The approaches are based on approximating the probability distributions by 1) orthogonal expansion and 2) a product of low order conditional probabilities. Only binary measurements are considered. Rademacher-Walsh functions are used as the orthogonal basis. A notion of tree dependence is introduced to effect the approximation by the product of low order conditional probabilities. The chain dependence and the 2-dimensional neighbor, or mesh, dependence are two instances of the tree dependence.