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ttribute and same cut A decision tree isdeveloped with the data set of time t. At time tþk, notonly is the same attribute as in the tree of time t usedbut also the same cut point in the tree of time t at eachstep of the partitioning. If the algorithm has not reached theleaf node of a particular branch of the tree, the tree of timetþk needs to go beyond the depth of the correspondingbranch in the tree of time t.Rule sets of time t and time tþkare generated based on the decision trees of time t and timetþk respectively. In the case of the same attribute and samecut in time tþk, a similar procedure is performed but adecision tree of time tþk is developed first.4.2.2. New decision tree Decision trees are generatedrespectively using the data set of time t and that of timetþk. Two rule sets are generated from the two decisiontrees of time t and time tþk. The added rules or perishedrules are usually found on the basis of this method.4.3. Discovery of a changed ruleIn this phase, three types of changed rules are detected by rulematching based on syntactic comparison. The inputs of phaseII are discovered rule sets at time t and tþk and the RMTwhich is specified by the user. For the explanation of our rulematching method, some notations are briefly defined.dij difference measure: degree of difference between rtiand rtþkj (–1rdijr1)sij similarity measure: degree of similarity between rtiand rtþkj (0rsijr1)‘ij degree of attribute match of the conditional parts‘ij ¼Aij maxð Xti ; Xtþkj Þcij degree of attribute match of the consequent partscij ¼1 if same consequent attribute0 otherwise Aij number of attributes common to the conditionalparts of both rtiand rtþkjGeneration of Decision TreeInput : D,Dt+k, Support ThresholdOutput : Rt,Rt+kPHASE IDiscovery of Changed Rule using RuleMatching MethodMeasuring the Degree of ChangeInput : Changed rule setPHASE IIPHASE IIIOutput : Significantly changed rule setInput : Rt,Rt+k, RMT (Rule Matching Threshold)Output : Changed rule set for each type of changeFigure 2: Overall procedure to detect change.Expert Systems, September 2005, Vol. 22, No. 4
Xti number of attributes in the conditional parts of rti Xtþkj number of attributes in the conditional parts of rtþkjxijk degree of value match of the kth matching attributein Aijxijk ¼1 if same value0 otherwise yij degree of value match of the consequent attributeyij ¼1 if same value0 otherwise Now we provide a similarity measure as follows, adaptedfrom the study of Liu and Hsu (1996).sij ¼‘ijPk2AijxijkcijyijAij if Aij 6¼ 00 if Aij ¼08><>:In sij; ‘ijPk2Aijxijk= Aij represents a similarity of theconditional part and cijyij represents a similarity of theconsequent part between rtiand rtþkj . If the conditional andconsequent parts between rtiand rtþkj are the same, then thedegree of similarity becomes 1. The similarity measure cantake any value between 0 and 1. Also the maximumsimilarity value is defined as follows.si ¼maxðsi1; si2; . . . ; sijRtþkjÞmaximum similarity value of rtisj ¼ maxðs1j ; s2j ; . . . ; sjRt jjÞmaximum similarity value of rtþkjThe maximum similarity value indi