On the applicability of modern algebra techniques to adaptive pattern recognition

摘要

The properties and algebraic structure of error correcting codes are shown to be applicable to adaptive pattern recognition. Mappings to encode pattern classes into a linear vector space are discussed. The relationship of that space to a polynominal ring with its ideal and cosets is developed, and features and pattern classes are presented in terms of their contribution to the elements of the vector space.The concept that each feature conveys information and thus has entropy is developed in its relation to candidate vectors and their joint information with ideal elements.The redundancy of feature information is utilized, and a decision algorithm is postulated upon the basis of a criterion of maximum joint entropy in excess of a calculable minimum. The correspondence of the decision criterion to a maximum likelihood decision is noted, and its relation to a learning algorithm is presented.The methodology appears to be general but requires a determination of the information value of features. A hierarchical network structure for higher order recognition sequences is an extension of the methodology presented, but work in this area is not yet sufficiently complete for presentation.