Structural pattern recognition, homomorphisms, and arrangements

Abstract

This paper discusses the general supervised pattern discrimination problem from a structural point of view. We show that both the problem of determining a decision rule and the problem of applying a decision rule are problems of finding homomorphisms, whether the pattern data structure is an N-tuple as in statistical pattern recognition, or a string or its generalizations as in syntactic pattern recognition. We then introduce the concept of an arrangement, which is a labeled N-ary relation, as a more complex pattern data structure and show how decision rules can be constructed and applied to arrangements using the homomorphism concept. The methodology suggested in the paper provides a structural pattern recognition generalization to phrase-structured syntactic pattern recognition.