Quality of Association Rules by Chi-Squared Test

Quality of Association Rules by Chi-Squared Test

Wen-Chi Hou (Southern Illinois University, USA)
Copyright: © 2009 |Pages: 7
DOI: 10.4018/978-1-60566-010-3.ch250
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Mining market basket data (Agrawal et al. 1993, Agrawal et al. 1994) has received a great deal of attention in the recent past, partly due to its utility and partly due to the research challenges it presents. Market basket data typically consists of store items purchased on a per-transaction basis, but it may also consist of items bought by a customer over a period of time. The goal is to discover buying patterns, such as two or more items that are often bought together. Such finding could aid in marketing promotions and customer relationship management. Association rules reflect a fundamental class of patterns that exist in the data. Consequently, mining association rules in market basket data has become one of the most important problems in data mining. Agrawal et al. (Agrawal, et al. 1993, Agrawal et al. 1994) have provided the initial foundation for this research problem. Since then, there has been considerable amount of work (Bayardo et al. 1999, Bayardo et al. 1999, Brin et al. 1997, Han et al. 2000, Park et al. 1995, Srikant et al. 1995, Srikant et al. 1997, Zaki et al. 1997, etc.) in developing faster algorithms to find association rules. While these algorithms may be different in their efficiency, they all use minsup (minimum support) and minconf (minimum confidence) as the criteria to determine the validity of the rules due to their simplicity and natural appeals. Few researchers (Brin et al. 1997, Aumann et al. 1999, Elder, 1999, Tan et al. 2002) have suspected the sufficiency of these criteria. On the other hand, Chi-squared test has been used widely in statistics related fields for independence test. In this research, we shall examine the rules derived based on the support-confidence framework (Agrawal et al. 1993, Agrawal et al. 1994) statistically by conducting Chi-squared tests. Our experimental results show that a surprising 30% of the rules fulfilling the minsup and minconf criteria are indeed insignificant statistically.
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The task of mining association rules is first to find all itemsets that are above a given minimum support ratio (minsup). Such itemsets are called large or frequent itemsets. Then, association rules are derived based on these frequent itemsets. For example, both {A, B, C, D} and {A, B} are frequent itemsets. The association rule, AB=>CD, is derived if at least c% of the transactions that contain AB also contain CD, where c% is a pre-specified constant called minimum confidence (minconf).

Support-Confidence Framework

We use the example in (Brin et al. 1997) to illustrate the support-confidence framework (Agrawal, et al. 1993, Agrawal et al. 1994). Suppose there are totally 100 transactions. 25 transactions buy tea and among them, 20 transactions also buy coffee. Based on the support-confidence framework, the rule ‘tea=> coffee’ has a support of 20% (20 / 100) and a confidence of 80% (20 / 25). Suppose minsup =5% and minconf =60%. Then, the rule is validated by the framework.

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