Group-theoretical vector space model

Abstract

This paper presents a group-theoretical vector space model (VSM) that extends the VSM with a group action on a vector space of the VSM. We use group and its representation theory to represent a dynamic transformation of information objects, in which each information object is represented by a vector in a vector space of the VSM. Several groups and their matrix representations are employed for representing different kinds of dynamic transformations of information objects used in the VSM. We provide concrete examples of how a dynamic transformation of information objects is performed and discuss algebraic properties involving certain dynamic transformations of information objects used in the VSM.