Property of H(A/C)If A is completely dependent on C, what is H(A/C)?In the extreme case, whenever C=yes, A is true; whenever C=no,A=false.Pr(C=yes and A=true)=1 Pr(C=yes and A=false)=0H(A/C)=?The other extreme: if A is completely independent on C, whatis H(A/C)?Pr(...) between 0 and 1,H(A/C)=??
Property of H(A|C) n If A is completely dependent on C, what is H(A|C)? n In the extreme case, whenever C=yes, A is true; whenever C=no, A=false. n Pr(C=yes and A=true)=1 n Pr(C=yes and A=false)=0 n H(A|C)=? n The other extreme: if A is completely independent on C, what is H(A|C)? n Pr(.) between 0 and 1, n H(A|C)=??
ExtendingtotwoattributesFor A1 and A2, we simply consider the Cartesianproduct of their valuesThis gives a single attributeThen we measure the dependency of A1A2 (a newattribute) on class CExample: Consider A1=Humidity and A2=WindyClass= PlayHumidity=(high, normal)Windy={True, False}A1A2=HumidityWindy={hightrue, highfalse, normaltrue,normalfalse)
Extending to two attributes n For A1 and A2, we simply consider the Cartesian product of their values n This gives a single attribute n Then we measure the dependency of A1A2 (a new attribute) on class C n Example: Consider A1=Humidity and A2=Windy, Class= Play n Humidity={high, normal} n Windy={True, False} n A1A2=HumidityWindy={hightrue, highfalse, normaltrue, normalfalse}
PlayHumidityHumidityWindyPlayHumidity WindyhighhighFALSEnohighFALSEnohighhighTRUEnohighTRUEnohighhighFALSEyeshighFALSEyeshighhighFALSEyeshighFALSEyesnormalnormal FALSEyesnormal FALSEyesnormalnormal TRUEnonormal TRUEnonormalnormal TRUEyesnormal TRUEyeshighhigh FALSEnohigh FALSEnonormalnormal FALSEyesnormal FALSEyesnormalnormal FALSEyesnormal FALSEyesnormalnormal TRUEyesnormal TRUEyeshighhigh TRUEyeshigh TRUEyesnormalnormal FALSEyesnormal FALSEyeshighhigh TRUEnohigh TRUEno
Humidity HumidityWindy Play high highFALSE no high highTRUE no high highFALSE yes high highFALSE yes normal normal FALSE yes normal normal TRUE no normal normal TRUE yes high high FALSE no normal normal FALSE yes normal normal FALSE yes normal normal TRUE yes high high TRUE yes normal normal FALSE yes high high TRUE no HumidityWindy Play highFALSE no highTRUE no highFALSE yes highFALSE yes normal FALSE yes normal TRUE no normal TRUE yes high FALSE no normal FALSE yes normal FALSE yes normal TRUE yes high TRUE yes normal FALSE yes high TRUE no