PATTERN RECOGNITION VIA MATCH CODED PATTERNS AND FEATUR,E VECTORS
Luan Ling Lee, Blanca R. M. Sosat · 1991
This paper describes a novel approach for pattern recognition based on t he matching be- tween coded patterns to feature vectors. Our intent is to integrate three individual steps (data acquisition, feature extraction and decision making) of a pattern recognition problem and to solve them simultaneously as a unique problem. The proposed pattern recogni- tion method was explicitly illustrated by a numerical character recognition problem. Coded patterns matched to feature vectors in a pat- tern recognition system is conceptually analogous with the matching between a group and a set of signal in a digital communication system. In order to get a set of signals matched to a group it is necessary to set up a cor- respondence between the linearity and the distance mea- sure. Such arrangement allows us to replace the Ham- ming distance measure by the Euclidean distance mea- sure (1). Now we define formally the matching of a set of signals to a group (Definition 1) and the transitive group (Definrtion 2). Definition 1 (l): A signal set S is matched to a group G if there exists a mapping h from G onto S such that, for any gi and g2 in G, d(lz(gi), h(gz)) = d(h(g;' *92), h(e)), where e denotes unit of G. A mapping h satisfying this condition will be called a matched mapping. Moreover, if h is one-to-one then its inverse, h-', will be called a matched labeling. Definition (l): Let S be a set of signals and f : S -+ S be an isometry. If A is a group of transformations of S and s is an element of S, then orbzt of s under A is the set A(s) = {f(s) : f A}. The transformation group A is called transitive of A(s) = S for some s E S (therefore, for all s E S). Next we consider only the case of set of signals with order an. The first Sylow's Theorem which guarantees the exiistence of a group of order 2n is as follows. First Sylow's Theorem (2): Let G be a finite group of order prim, n 1 and p does not divide m. Then, (1) G has a subgroup of order pz for any integer i, 1 5 i 5 n; (2) Each $order subgroup H of G is a normal group of order pi+' for 1 5 i 5 n. The existence of a subgroup of order 2 allows us to form a group of 2 orthogonal matrices which is capable of generating a transitive group. It is worth mentioning that the product between each element of the group of matrices and a signal vector (feature vector) results in a signal vector (feature vector) also. Nulmerical pat tern recognition: Each input pat- tern (numerical character) is an 4-by-8 pixel rectangle.