A topological approach to representational data models

Abstract

As data accumulate faster and bigger, building representational models has turned into an art form. Despite sharing common data types, each scientific discipline often takes a different approach. In this work, we propose representational models grounded in the mathematics of algebraic topology to understand foundational data types. We present hypergraphs for multi-relational data, point clouds for vector data, and sheaf models when both data types are present and interrelated. These three models use similar principles from algebraic topology and provide a domain-agnostic framework. We will discuss each method, provide references to their foundational mathematical papers, and give examples of their use.