On the complexity of inducing categorical and quantitative association rules

TL;DR

This paper analyzes the computational complexity of inducing both categorical and quantitative association rules, highlighting the challenges and specific cases in data mining applications like market basket analysis.

Contribution

It formally defines the problem of quantitative association rule mining and provides a detailed complexity analysis for various special cases.

Findings

Inducing association rules is computationally complex in general.

Certain cases like fixed-size attribute databases are computationally easier.

Null values and sparsity impact the complexity of rule induction.

Abstract

Inducing association rules is one of the central tasks in data mining applications. Quantitative association rules induced from databases describe rich and hidden relationships holding within data that can prove useful for various application purposes (e.g., market basket analysis, customer profiling, and others). Even though such association rules are quite widely used in practice, a thorough analysis of the computational complexity of inducing them is missing. This paper intends to provide a contribution in this setting. To this end, we first formally define quantitative association rule mining problems, which entail boolean association rules as a special case, and then analyze their computational complexities, by considering both the standard cases, and a some special interesting case, that is, association rule induction over databases with null values, fixed-size attribute set databases, sparse databases, fixed threshold problems.