Determining concepts by group membership

Abstract

One contribution of this paper is an efficient algorithm for deciding membership in a subgroupH of an Abelian groupG whenG andH are in a special form. Our approach is particularly fast because calculations are postponed until needed, and because some decisions can be made based on the existence of certain objects without actually calculating them. This mathematical problem arises naturally in machine learning, and is particularly relevant to concept modeling. We use genetic algorithms as a nontrivial example of how concept formation may correspond to subgroup formation and to illustrate that analysis may reveal abstract concepts determined by group membership which are not initially apparent. This example forms another contribution of this paper; genetic search has not previously been framed within an algebraic context.