Introduction of Empirical Topology in Construction of Relationship Networks of Informative Objects

TL;DR

This paper introduces empirical topology, a novel system-theoretic measure for discovering relationships between objects in data, demonstrated through application to an astronomical database.

Contribution

It presents a new method for relationship discovery based on empirical topology, advancing data mining techniques for analyzing object relationships.

Findings

Effective relationship detection in astronomical data

Empirical topology provides meaningful object proximity measures

Method shows promising results in real-world data analysis

Abstract

Understanding the structure of relationships between objects in a given database is one of the most important problems in the field of data mining. The structure can be defined for a set of single objects (clustering) or a set of groups of objects (network mapping). We propose a method for discovering relationships between individuals (single or groups) that is based on what we call the empirical topology, a system-theoretic measure of functional proximity. To illustrate the suitability and efficiency of the method, we apply it to an astronomical data base.