by Brin et al. Because of the limitation of confidence, Brin et al.  had proposed the idea of using interest factor as a measure of interesting- ness. The all-confidence measure was proposed by Omiecinski . Xiong et al.  introduced the cross-support property and showed that the all- confi.dence measure can be used to eliminate cross-support patterns. A key difficulty in using alternative objective measures besides support is their lack of a monotonicity property, which makes it difficult to incorporate the mea- sures directly into the mining algorithms. Xiong et al.  have proposed an efficient method for mining correlations by introducing an upper bound function to the fcoefficient. Although the measure is non-monotone, it has an upper bound expressign that can be exploited for the efficient mining of strongly correlated itempairs.
Fabris and Fleitas  have proposed a method for discovering inter- esting associations by detecting the occurrences of Simpson’s paradox . Megiddo and Srikant  described an approach for validating the extracted
396 Chapter 6 Association Analysis
patterns using hypothesis testing methods. A resampling-based technique was also developed to avoid generating spurious patterns because of the multiple comparison problem. Bolton et al.  have applied the Benjamini-Hochberg
 and Bonferroni correction methods to adjust the p-values of discovered patterns in market basket data. Alternative methods for handling the multiple comparison problem were suggested by Webb  and Zhang et al. .
Application of subjective measures to association analysis has been inves- tigated by many authors. Silberschatz and Tuzhilin  presented two prin-
ciples in which a rule can be considered interesting from a subjective point of view. The concept of unexpected condition rules was introduced by Liu et al. in 12771. Cooley et al.  analyzed the idea of combining soft belief sets using the Dempster-Shafer theory and applied this approach to identify contra- dictory and novel association patterns in Web data. Alternative approaches include using Bayesian networks  and neighborhood-based information
[2a5] to identify subjectively interesting patterns. Visualization also helps the user to quickly grasp the underlying struc-
ture of the discovered patterns. Many commercial data mining tools display the complete set of rules (which satisfy both support and confidence thresh- old criteria) as a two-dimensional plot, with each axis corresponding to the antecedent or consequent itemsets of the rule. Hofmann et al.  proposed using Mosaic plots and Double Decker plots to visualize association rules. This approach can visualize not only a particular rule, but also the overall contin- gency table between itemsets in the antecedent and consequent parts of the rule. Nevertheless, this technique assumes that the rule consequent consists of only a single attribute.
Association analysis has been applied to a variety of application domains such as Web mining 1296,3L71, document analysis 1264], telecommunication alarm diagnosis , network intrusion detection 1232,244,275], and bioinformatics
1302, 3271. Applications of association and correlation pattern analysis to Earth Science studies have been investigated in [298, 299, 319].
Association patterns have also been applied to other learning problems such as classification1276,278], regression , and clustering1257,329,332]. A comparison between classification and association rule mining was made by Freitas in his position paper . The use of association patterns for clustering has been studied by many authors including Han et al.l257l, Kosters et al. 12721, Yang et al.  and Xiong et al. .
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