A Category Theoretical Investigation of the Type Hierarchy for Heterogeneous Sensor Integration

TL;DR

This paper explores using category theory and sheaf theory to unify and integrate heterogeneous sensor data types, enabling more comprehensive information gathering from diverse sources.

Contribution

It introduces a novel approach to interpret arbitrary sensor outputs as vector spaces within a categorical framework for data integration.

Findings

Sheaf theory provides a canonical framework for sensor data integration.

Interpreting sensor outputs as vector spaces facilitates data combination.

The approach enhances robustness and completeness of information from diverse sensors.

Abstract

Consider the case of many sensors, each returning very different types of data (e.g., a camera returning images, a thermometer returning probability distributions, a newspaper returning articles, a traffic counter returning numbers). Additionally we have a set of questions, or variables, that we wish to use these sensors to inform (e.g., temperature, location, crowd size, topic). Rather than using one sensor to inform each variable we wish to integrate these sources of data to get more robust and complete information. The problem, of course, is how to inform a variable, e.g., crowd size, using a number, a newspaper article, and an image. How do we integrate these very different types of information? Michael Robinson proposes that sheaf theory is the canonical answer. Moreover, one of the axioms in Robinson's paper which makes sheaf theory work for data integration is that all data sources have the structure of a vector space. Therefore, the motivating question for everything in this report is "How do we interpret arbitrary sensor output as a vector space with the intent to integrate?"