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al., 1997, 1998; Han et al., 1999).Das et al. (1998) consider the problem of findingrules relating patterns in a time series to other patternsin that series, or patterns in one series to patterns inanother series. Han et al. (1999) present several algorithmsfor efficient mining of partial periodic patterns, byexploring some interesting properties related to partialperiodicity. Das et al. (1997) also present an intuitive modelfor measuring the similarity between two time series. Butthese studies are rather different from our research whichfocuses on the detection of irregularity rather thanregularity in data.The fifth research field is mining class comparisons todiscriminate between different classes (Bay & Pazzani,1999; Ganti et al., 1999; Han & Kamber, 2001). Ganti et al.(1999) present a general framework for measuring changesin two models. Essentially, the difference between twomodels is quantified as the amount of work required totransform one model into the other. Their frameworkcovers a wide variety of models, including frequent itemsets, decision tree classifiers and clusters, and capturesstandard measures of deviation such as misclassificationrate and the w2 metric as special cases. But it cannot bedirectly applied to detect customer behavior changesbecause it does not provide which aspects have changedand what kind of changes have occurred. Bay and Pazzani(1999) and Han and Kamber (2001) also provide techniquesfor understanding the differences between severalcontrasting groups. But these techniques can only detectchange about the same structured rule.Finally, Liu et al. (2000) present a technique for changemining by overlapping two decision trees generated fromdifferent time snapshots. In a decision tree, each path fromthe root node to a leaf node represents a hyper rectangleregion. A decision tree essentially partitions the data spaceinto different class regions. Changes in the decision treemodel thus mean changes in the partition and changes inthe error rate. Our object in change mining is to discoverthe changes in the new data with respect to the old data andthe old decision tree, and present the user with the exactchanges that have occurred. However, their researchcannot identify how much change has occurred. If thereare a large number of changes, their methodology cannotrank what the most significant changes are. Song et al.(2001) developed a change detection system based onassociation rule mining. However, the application ofassociation rule mining and decision trees is different.Change detection based on association rule mining can beused to identify changes of customer behavior in unstructuredand ill-defined situations because of the unsupervisedlearning feature of association rulemining. However, usingdecision trees in the change detection problem can be usedin more structured situations in which the manager hasspecific research questions and it also detects the change ofclassification criteria in a dynamically changing environment.3. ProblemIn this section, we examine all possible types of changebased on past research and business requirements (Liu &Hsu, 1996; Liu et al., 1997; Suzuki, 1997; Dong & Li, 1999;Lanquillon, 1999; Padmanabhan & Tuzhilin, 1999; Songet al., 2001). After that, each type of change and changeExpert Systems, September 2005, Vol. 22, No. 4
detection problem is defined. Let us define the followingnotation.Dt, Dtþk data sets at time t, tþkRt, Rtþk discovered de