Decomposition of quantitative Gaifman graphs as a data analysis tool

TL;DR

This paper explores the use of Gaifman graphs and their decompositions as a novel method for exploratory data analysis, especially suited for multirelational data, by extending them with quantitative information.

Contribution

It introduces generalized Gaifman graphs with quantitative data and demonstrates their utility in revealing data insights through modular decompositions.

Findings

Gaifman graph decompositions reveal interesting data patterns

Enhanced Gaifman graphs enable more comprehensive analysis

Approach is suitable for multirelational data frameworks

Abstract

We argue the usefulness of Gaifman graphs of first-order relational structures as an exploratory data analysis tool. We illustrate our approach with cases where the modular decompositions of these graphs reveal interesting facts about the data. Then, we introduce generalized notions of Gaifman graphs, enhanced with quantitative information, to which we can apply more general, existing decomposition notions via 2-structures; thus enlarging the analytical capabilities of the scheme. The very essence of Gaifman graphs makes this approach immediately appropriate for the multirelational data framework.