Quantitative Association Rules: Complexity Analysis and Implications

Title: Quantitative Association Rules: Complexity Analysis and Implications

Abstract: This research paper focuses on the complexity of inducing quantitative association rules, a crucial task in data mining applications. The authors define the problem and analyze its computational complexities, considering both standard cases and special ones like association rule induction over databases with null values, fixed-size attribute set databases, sparse databases, and fixed threshold problems. The paper aims to provide insights into the computational characteristics of the problem, which can help identify tractable cases and develop more effective algorithms.

Main Research Question: How complex is it to induce quantitative association rules from databases, and what are the implications of this complexity?

Methodology: The authors first define the problem of quantitative association rule induction and provide a formal description. They then analyze the computational complexities of the problem, considering various scenarios. The analysis is based on the use of indices, which are functions with values usually in [0, 1], used to measure the validity of the extracted association rules. The authors consider both the standard cases and special cases, such as databases with null values, fixed-size attribute set databases, sparse databases, and fixed threshold problems.

Results: The results of the complexity analysis reveal that the problem of inducing quantitative association rules can be computationally challenging. However, the authors identify tractable cases and hard complexity sources. They also provide insights into the implications of this complexity, which can help in developing more effective algorithms for data mining applications.

Implications: The findings of this research have significant implications for the field of data mining. By understanding the computational complexities involved in inducing quantitative association rules, researchers and practitioners can develop more efficient algorithms and identify potential areas for further research. Additionally, the results can help in the development of better strategies for knowledge discovery in databases, which can ultimately lead to improved decision-making processes in various application contexts.

Link to Article: https://arxiv.org/abs/0111009v1 Authors: arXiv ID: 0111009v1