A fundamental question of counting in association rules

Discovery association rules (D-AR) are widely used for data mining in industry, and have been extensively researched in academia. An elementary step in the calculation of the strength of each proposed rule X→Y is the tabulation of occurrences and co-occurrences of X and Y. Yet, a fundamental question does not appear to have received attention in the literature. The question is, how should one count these occurrences? Nearly all researchers and practitioners use one method, but there is actually an alternative way to count, and the data mining literature has not seriously considered the alternative or justified the prevailing choice. This fundamental question of counting is not a purely theoretical difference; the methods yield different results. In this research, we investigate the implications of the two methods. Results include the following: (1) Both methods can be correct under different probabilistic setups; (2) The two counting methods yield different results, in terms of the ranking of rules by their strengths; (3) The extent to which the methods diverge depends on properties of the data, one of which we identify; (4) Based on analytical and empirical results, we propose a set of guidelines for making a principled choice of counting method in a given study. Our research provides the basis for choosing an appropriate D-AR counting method, and improves our understanding of how this choice affects the meaning, strengths, and limitations of results.