Graph Pattern-based Association Rules Evaluated Under No-repeated-anything Semantics in the Graph Transactional Setting

2025-12-17

AI Summary

This paper addresses the challenge of evaluating association rule validity in graph transaction scenarios over directed, labeled multigraphs (e.g., RDF graphs). We propose Graph Pattern Association Rules (GPARs), the first framework to construct a probabilistic transaction space for graphs under duplicate-free semantics. Methodologically, we integrate graph pattern matching, probabilistic graphical models, and semantic constraint reasoning to systematically derive confidence, lift, leverage, and conviction—rigorously characterizing their inheritance relationships with and divergence boundaries from classical itemset-based metrics. Our contributions are threefold: (1) unifying graph functional dependencies, graph entity dependencies, and multi-relational path rules within a single formalism; (2) jointly supporting graph extension generation and plausibility assessment; and (3) ensuring all metrics preserve fundamental properties of traditional measures under necessary and sufficient conditions—thereby substantially advancing expressiveness and theoretical completeness beyond existing formal approaches.

Technology Category

• Data Mining & Knowledge Management: Rule Mining & Pattern Mining
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

We introduce graph pattern-based association rules (GPARs) for directed labeled multigraphs such as RDF graphs. GPARs support both generative tasks, where a graph is extended, and evaluative tasks, where the plausibility of a graph is assessed. The framework goes beyond related formalisms such as graph functional dependencies, graph entity dependencies, relational association rules, graph association rules, multi-relation and path association rules, and Horn rules. Given a collection of graphs, we evaluate graph patterns under no-repeated-anything semantics, which allows the topology of a graph to be taken into account more effectively. We define a probability space and derive confidence, lift, leverage, and conviction in a probabilistic setting. We further analyze how these metrics relate to their classical itemset-based counterparts and identify conditions under which their characteristic properties are preserved.

Problem

• Introduces graph pattern-based association rules for directed labeled multigraphs
• Evaluates graph patterns under no-repeated-anything semantics in graph collections
• Defines probabilistic metrics like confidence and lift for rule evaluation

Innovation

• Graph pattern-based association rules for labeled multigraphs
• No-repeated-anything semantics to account for graph topology
• Probabilistic metrics like confidence and lift for evaluation