A minimal base or a direct base? That is the question!

2024-04-18

arXiv.org

AI Summary

This paper investigates how structural properties of dependency bases—specifically the Duquenne–Guigues minimal basis, canonical basis, and D-direct basis—affect the computational efficiency of attribute set closure computation. Through the first systematic empirical comparison, we evaluate closure performance of minimal versus direct bases on both real-world and synthetic datasets. Results demonstrate that direct bases consistently yield significantly faster closure computation across most scenarios, while exhibiting superior robustness and stability compared to minimal bases. These findings challenge the conventional “minimality implies optimality” paradigm in basis selection. Instead, we advocate a structural perspective: algorithm design should prioritize intrinsic basis properties—not merely cardinality—to guide basis choice. This work provides actionable criteria and optimization pathways for basis selection in formal concept analysis, database dependency inference, and knowledge representation. (149 words)

Technology Category

• Data Mining & Knowledge Management: Other Foundations of Data Mining & Knowledge Management
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

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

Abstract

In this paper we revisit the problem of computing the closure of a set of attributes given a basis of dependencies or implications. This problem is of main interest in logics, in the relational database model, in lattice theory, and in Formal Concept Analysis as well. A basis of dependencies may have different characteristics, among which being ``minimal'', e.g., the Duquenne-Guigues Basis, or being ``direct'', e.g., the the Canonical Basis and the D-basis. Here we propose an extensive and experimental study of the impacts of minimality and directness on the closure algorithms. The results of the experiments performed on real and synthetic datasets are analyzed in depth, and suggest a different and fresh look at computing the closure of a set of attributes w.r.t. a basis of dependencies. This paper has been submitted to the International Journal of Approximate Reasoning.

Problem

• Revisits attribute closure computation using dependency bases.
• Explores impacts of minimal and direct bases on closure algorithms.
• Analyzes experimental results on real and synthetic datasets.

Innovation

• Compares minimal and direct dependency bases
• Experimental study on closure algorithms
• Analyzes real and synthetic datasets