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11/21/2014 & ! - ! ! " # $ $ ! ! &'() * %$ + , / 11/21/2014 2 11/21/2014 2.# : ! #*5 ; # ! " 6*%" 6 ! ! ) ! ! # 6# 65 6" 6$ 6" ! # 6" 6$ 6# ! 87 ! ! 7 ) 99, 11/21/2014 ,9 ,, ?< + < !< @ = ! + < ! > = ! 11/21/2014 L + B @ ! A ! H CA @ ! = + < = ! - ! @ C ! C + < : ! + !C &= 1I + < 49I !A 7< ! = H CA + < = ! J K = D E > ! < > F ! G = C ! H< ! @ = @ ) : ! A ! < E ! - ! ! - ! + < - ! C = ! =! ! A ME + K # ?: ! +S ( = 5< E T C: ! +S # ! L < S+ + < = ! C: ! +S D : D ! A ! U AK ! < N - ! < C ) = + < = !C R N A = - ! ! ! + AK ! #*5 J + < = ! ! ! J CK ! + = G = ! !!D ! : ! @ 6 6 > #K J !D N O !+ < = ! C N G < !< P !C ! + < = ! N Q> !C ! E = P ! ! = > R N H : ! ! = C R + < = ! N H GE ! < ) + ! N : ! @ + < = ! J + < = ! @ < C CA E L < A : M M > ! ! + L = ! J ! G E + < J E < M M @ = ! 11/21/2014 ? + CA + E ?A C C ! B ! ?P " C A ! L E ! < : !) ?A S D !A ! < ! < V L - ! !! ! M ! < , J ) < @ F ! = < ! ! ! < 7< > + < = C ! J CA ! < / = ! ! A = ! J ) < + !< = J J ! C< ! < = : ! 7@ + ! = ! < 7@ < @ + ! @ + A ) W ! - ! ! @ A ? C H # G < ! E > ! # < ! = = @ + ! @ 11/21/2014 H< P !C + < = ! = + < = ! ! 7M ) ! D) ) = G - M ! ! P !C G - ! 7" C X E H< @ ! !< < < + # * < < H< O! @ C )" C < " @ V + ! !) ! ! @ = + ! " ! C ! O! @ E ! : ! - ! C ) G ! @ O! @ ! > ) ! ? E C + < = ! @ ! @ ! @ C + K + A ! J + < J E = J " ! @ J ! E @ ! # = = ! J # ! = ! # + ! ! + ! @ " ! )B S ! - ! = ! ) ) J < < F !+ ) = )E CA + > )E ) CJ 11/21/2014 , Q< C ! @ , " = J % ) CR CA CG + < " K = - ! CA C @ CJ - ! C CR CA + + ! @ ! / & ! ! < E = + + C < ! @ " " - ! C H G B< ! > ) 6L - ! A !A A !) G J ! < + < ! = 7= + E ! !A CA E > C K CK ! ) B< T ! H - ! M ! @ < 7= CA E C !D C E N (< < !A E S + - ! !A ! @ + < )! G X = !) D G ) $ + M - ! H ) M = NH C + ) M 7= ! @ G ! ! K Y H ! @ - ! ! CA +Z + - ! ! +@ - ! = A E Y + < O ! C A ! C L < & - ! C ) C ! K) S + ' ! O N #< - ! A ! ! < E L ) @ ! A X < C + < = !B @ E < M ! @ & C< K " ! < > ! A ! L - ! ! #J = + < C J !) # G ) AK ! C ! - ! ! ( # E N N " L ! - ! < > C J CA C ! [ F !C O J N H 48, !A N L < + G C C G F ! A / + C + N N ? N F ! K7 ! ) A ! ! ! ! ! J !7 = + ! + - ! ! F C 11/21/2014 \ O! E SE #*5 + < Y S < E = ! '& * $# P ! Y S Y P + T +G C = ! S M = ! C ! AK ! < + + 7< + < = ! ! &'O > 'O'&] $ G C C ! < + ! #> E < D / C = < D @ OD ! OD OD < D ! @ !!< C > > ! @ O < #> E ! < C !C = < G # "& #i J CA ! D ! D < G ! ! > > C + " =E S > C< ! ! ' C ! J < = @ C + - !C #J != W ! K ! A ! > @ > + - !C #J - ) + - ! M S !M = ' ! C K) = > ! > @ @ " = A J > @ != ! < - ! 7< C C < B + = !A (C K ! ? C CJ) CA + < = !E C K = M B J < ! G = CJ + - ! = ! ) - ! + ! ) > ) A ! O C !C ^ ? #J ! J V + - ! = @ = !A C K ! = - CJ " CA ! ,0 P ! = 11/21/2014 ! " ! # ! $ % ! & ! ! ! L + = K ! _ )+ = + - ! _ * ] ! O U O ! ] K + O U + ] 10 11/21/2014 L + = K ! _ )+ = + - ! _ * ! O O D C !< ] _ ! < AK ! D < = U ! ] O _ +` ∧U _ U + + ∧ ` 'O" ` = ) ∨ ` _* ` * O U `U U ] + _ O * O ! ! G ] O G + _ ! K + O + ] 11 11/21/2014 _ +` ∨U _ * U U ! U O _ ∨_ ∨ _ +` +`_ +`* + ! ] O ∧U `U _ + ] * U O ! ] + + ] O U `O ∧ _ ! + + _ ] `U O U + ] #> CA ! @ B ! A * J < G ! #< ! > # G C > = < < G CA @ C C ! +@ ) C C ) B> ! > E C < < 12 11/21/2014 ? ! ! + < D < L - ! P K = D G L - ! P = J = F ! F !C > D /4 ? C C = G G G CA E < M J " A ! F ! - ! $ > > #J C C , ? H #J < # H H ! ! #J C H < G C ! G ! C < ! H B G = !< C < G ! J ! > !< G 13 11/21/2014 A ! < i a,) ;) b - ! ! C m i =1 G ' J < !< a ,) G 'C > ) si s log i s s ;) b = a ,) n nb #i G ' ij n E(A) = ? i` > I(s1,s2 , ,sm ) = − "F ! ) ;) #i j =1 @ - ! j '` s1 j + + s mj > s < j I( s1 j , , smj ) ! G ' G(A) = I(s1 , s , , s m ) − E(A) ) < D ! G JC C > > ! " ! # ! $ % & ! ! ! ! 14 11/21/2014 J ` ,0 ` #, ` c] , ` \) d) # ` cO d `1 I(S1 , S2 ) = I(9,5) = − ! 9 5 log − log = 0.940 14 14 14 14 3 4 − log − log = 0.985 7 7 O e/f) 08g e2f) ,8g 6 1 − log − log = 0.592 7 7 N H D ? G !.1 ! G C ) ! !` 6 2 − log − log = 0.811 8 8 U U < + ! e2f) 8g e/f) /8g 3 3 − log − log = 1.000 6 6 N 15 11/21/2014 _ + _ e.f) /8g * e0f) 98g e/f) 8g !""# N N # H D t GINI(t ) = − = ,8, =9+ j ! CJ p ( j t ) = & < p( j t ) j + < ! D t > C @ < GINI(t ) = − p( j t ) j & " #, ` ` # ` 2 ` , H$O$ ` , N #, f # ` , N 9f, ` #, ` , # ` H$O$ ` , N , N ` 34 #, ` # ` H$O$ ` , N N ` 000 16 11/21/2014 L > T D p = k < CA G ! k GINIchia = ! CJ i =1 ni = n = A ! ni GINI(i ) n ! D i ! D p # G > " J H$O$chia < # ) = C > < ' p p " O, H O, `,8 `9 ,\0 H O `,8 , `9 1.4 ' H ' " @ chia (&) && `3 ,.h9 ,\0 f1 ,.h9 1.4 `9 /// (&) !< > " " O > @ = !< J < !< G < ! 'iv = 'jv #< !< v CK ! !< v ! # "& C G H J = !< JH " +T E * &&* #&* &* + % * " "&* # + &* $ $ * % # * & %&* B j 49L i 49L 17 11/21/2014 #< !< B # !< > # E v < !< : ! ! 7M = G !< ! !!< ! J > $ ( < #< A CA ! ! $ % &' $ % &' $1% &' $ % &' $ % &' ! * ] U O ! ] O C + _ O $^8 !! G CA T 'O" N = _ ! C ! ! ) !< @ T + D < ! @ G U O + ] !""# ∧ () *)+ ,! -" !""# ∧ -" ! *)+ ,! /+0 !""# 2+.3 *)+ ,! /+0 !""# $ ∧ " ( *)+ ,! -" !""# $ ∧ + # *)+ ,! /+0 18 11/21/2014 C $ > E C = ) + - ! C J B S J!< = J!< = @ C = - M ! C - M ! < + #> E K7 #> E ! #> E #J ! +@ #> E C ! # J ! = )+ > > > > ) ( !E E C C J B S A ! ! < A F ! ! > ) > )+ $ #> E C 85 ! @ D _*# 12 VVV B V ! " ! 7 ' k! k B " ' 13 19 11/21/2014 , / \ ,9 ,, , ,/ ,0 ,1 ,2 ,3 ,4 '"' V ' )$ 990 '"' l' VVV # + )& ) m # 991 !' ' l 8U )5 )_ # V! ) " 992 ^ #*5 $ ' n o^ 8 8 8#*58 $ % `,2\/,1 #Q_ $ 992 # ! l' ! V ! o ! o B " ) 991 ' ! % $5#l H E8 $ V ) O V ] +) O] 992 '7 l' VVV B V O ' 992 ! l' VVV B ! H )# 992 #*5 V l' n o#*58 V % `,\.4/ B n V )$ 992 )' %' #*5 % # ! V l ' VVV B n " )& 99 # * ! l' VVV V 7 V ! p04 B # 992 " #*5l ' VVV B O $ 992 O #*5fl ' VVV p _Oq V # 991 _ _O# l ' VVV _ B _ 992 l' VVV V 8 _ 992 U #*5l ' VVV V 8 V 8 ,\ 992 #*5 ! l' VVV B 992 #*5 ' + & l' V ! V )$ 992 # * ! l' VVV !B B /o `/9299999,9,, ' 992 ' l' VVV ! 992 # ! ,, #*5 V l' VVV 9.9 V V o5 $"`1% U+ 992 # ! l' V+ ! V+ # p p ! U ) 992 " # * ! l' V ! 9).4\4\/) \p! ,/123)99 ! , ./ )$ 8 # B ` B ! + 1\ 20
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