organization should not monotonically increase or decrease with the number of useful attributes. Because not all attributes,but only those with high significance are desired to appear in the final rules,a measure,Attribute Significance,is introduced. Definition 4:Attribute Significance is the ability of an attribute in determining the class name for an instance.The attribute significance of4 is labeled as S4,and the value of S is determined during the evolutionary process. As can be seen,S reflects the distribution of the values of in each class.In the evolutionary process,the value of S is identical for all populations so that all populations can coevolve.When populations evolve,S evolves also.The value of S4 is updated when computing the fitness of an organization.The details are shown in Algorithm 1. Algorithm 1 Attribute Significance t denotes the generation of the evolutionary process.The number of attributes is m.N is a predefined parameter.org is the organization under consideration and orge ORGr.Aj denotes the jth attribute in Forg. begin if (t=0)then for i:=1 to m do s =1.0; Determining Forgi Uorg:=0; for j:=1 to IForgl do begin Randomly selecting an organization org satisfying 11
11 organization should not monotonically increase or decrease with the number of useful attributes. Because not all attributes, but only those with high significance are desired to appear in the final rules, a measure, Attribute Significance, is introduced. Definition 4: Attribute Significance is the ability of an attribute in determining the class name for an instance. The attribute significance of A is labeled as SA, and the value of SA is determined during the evolutionary process. As can be seen, SA reflects the distribution of the values of A in each class. In the evolutionary process, the value of SA is identical for all populations so that all populations can coevolve. When populations evolve, SA evolves also. The value of SA is updated when computing the fitness of an organization. The details are shown in Algorithm 1. Algorithm 1 Attribute Significance t denotes the generation of the evolutionary process. The number of attributes is m. N is a predefined parameter. org is the organization under consideration and org∉ORGT. Aj denotes the jth attribute in Forg. begin if (t=0) then for i:=1 to m do :=1.0 i 0 SA ; Determining Forg; Uorg:=∅; for j:=1 to |Forg| do begin Randomly selecting an organization org′ satisfying
org.Member class org.Member class; if (AjEForg)and (the value of Aj in Ford is different from that of Aj in Forg)then Uor=UA else Reducing Si according to (1)(Casel); end; if(Uorg≠☑)then begin Randomly selecting Nexamples whose class names are different from org.Member class; if (the combination of the attribute values in Uorg does not appear in the N examples)then Increasing the attribute significance of all attributes in Uorg according to (1)(Case2) e1 se Uorg:=☑； end; end. 0.9S+0.05, Case1, S= (1) 0.9S+0.2, Case2. The parameter N not only ensures that the rules extracted from organizations are consistent to some extent,but also makes the algorithm robust against noise.If N is set to a larger value,the rule is more consistent,but the algorithm is more sensitive to noise.Since the value of S is restricted to the range of [0.5,2],it is set to 1.0 at the beginning,and updated during the evolutionary process.When the conditions of Casel in(1)are satisfied,S4 should
12 org′.Member_Class ≠ org.Member_Class; if (Aj∈Forg′) and (the value of Aj in Forg′ is different from that of Aj in Forg) then UUA org org j := ∪ else Reducing j t SA according to (1) (Case1); end; if (Uorg ≠ ∅) then begin Randomly selecting N examples whose class names are different from org.Member_Class; if (the combination of the attribute values in Uorg does not appear in the N examples) then Increasing the attribute significance of all attributes in Uorg according to (1) (Case2) else Uorg := ∅; end; end. 1 0.9 0.05, Case1, 0.9 0.2, Case2. t t A A t A S S S + + = + (1) The parameter N not only ensures that the rules extracted from organizations are consistent to some extent, but also makes the algorithm robust against noise. If N is set to a larger value, the rule is more consistent, but the algorithm is more sensitive to noise. Since the value of SA is restricted to the range of [0.5, 2], it is set to 1.0 at the beginning, and updated during the evolutionary process. When the conditions of Case1 in (1) are satisfied, SA should
be punished: S”=S-$-0.05 0.9S4+0.05 (2) 10 When the conditions of Case2 in (1)are satisfied,S should be awarded: s=S+2-S=0.9s+02 (3) 10 The conditions of Casel and Case2 are the ones required for rule extraction. The idea of Algorithm 1 is encouraged by the following observations.If the values of 4 do not concentrate in the same class,A has low significance.But if a combination of several attribute values is unique in a certain class,these attributes together have high significance. An example is shown to evaluate whether Algorithm 1 can correctly determine attribute significance. Example 2:Following Example 1,Fig.1 1.66-S1ZE ◆EYES 1.4 -HAIR shows the evolutionary process of the attribute 1.2 significance for the three attributes,where the x-coordinate stands for generations.As can be U.8 seen,after running 10 generations,the attribute 6 GEN Fig.I.Evolutionary process of the attribute significance can be differentiated completely. significance The significance of HAIR is the highest whereas that of SIZE is the lowest.This result agrees with that of decision trees,and illustrates the usefulness of Algorithm 1. On the basis of the attribute significance,the fitness function for organizations is defined as follows, 13
13 be punished: 1 0.05 0.9 0.05 10 t tt t A AA A S SS S + − =− = + . (2) When the conditions of Case2 in (1) are satisfied, SA should be awarded: 1 2 0.9 0.2 10 t tt t A AA A S SS S + − =+ = + . (3) The conditions of Case1 and Case2 are the ones required for rule extraction. The idea of Algorithm 1 is encouraged by the following observations. If the values of A do not concentrate in the same class, A has low significance. But if a combination of several attribute values is unique in a certain class, these attributes together have high significance. An example is shown to evaluate whether Algorithm 1 can correctly determine attribute significance. Example 2: Following Example 1, Fig.1 shows the evolutionary process of the attribute significance for the three attributes, where the x-coordinate stands for generations. As can be seen, after running 10 generations, the attribute significance can be differentiated completely. The significance of HAIR is the highest whereas that of SIZE is the lowest. This result agrees with that of decision trees, and illustrates the usefulness of Algorithm 1. On the basis of the attribute significance, the fitness function for organizations is defined as follows, Fig.l. Evolutionary process of the attribute significance