Pattern Recognition of Relational Structures

A new representation which abstracts relational characteristics of a class of structured data is introduced in this paper. The representation, called primitive relational structure, naturally becomes an element of Boolean algebra, the operations of which reflect the structural similarity and dissimularity of any two objects. Then on the Boolean algebra, distance and probability measures are defined. Further, to render a feasible scheme for estimating structural probability distribution where sample size of data class is relatively small in real world application, a second order approximation scheme of higher order probability on discrete-valued data is adopted. In such a scheme the optimal subset of features for the representation of the probability distributions are extracted by optimising certain information measures defined on the set of relations. The objective function for optimisation can be formulated to yield either (a) distributions that best approximate the high order probability of an ensemble or (b) distributions that lead to optimal discrimination between classes. Thus with the distance and probability measures defined, both unsupervised and supervised classification on PRS can be achieved by algorithms adapted respectively from (a) a discrete-value data clustering algorithm and (b) an error-probability minimax classification scheme. The proposed method has been applied to the analysis of structural and measurable patterns of discrete-time systems.