Group-theoretical vector space model

TL;DR

This paper introduces a novel group-theoretical vector space model that uses group actions and representation theory to model dynamic transformations of information objects within a vector space framework.

Contribution

It extends the traditional VSM by integrating group actions, enabling algebraic modeling of dynamic information transformations.

Findings

Demonstrates how group representations can model dynamic transformations.

Provides concrete examples of algebraic properties of transformations.

Shows the applicability of group theory in information object manipulation.

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.