Interestingness Measures for Association Patterns : A Perspective
Transcription
Interestingness Measures for Association Patterns : A Perspective
! " ## $ % # " " & ' ( $& # " ) # * ## #" " + % % $ " " # # " , % " % - , % % &# " # # " # & % # % Æ # # . ## / $ 0# ' 1*& 2 & 0# " ( Æ ' " # ( 3 % % # % & # # % " % Æ " ! " # $! % ! ! % & ' ()* + (* , + & ! # , -./ / ! ! % 0 )1 2 ) Æ! / -./ % 3 % ' ()* ! ( ,! * (* ( ,! * 4 ! 5 # &% ,! ! " ,! ! 6 ) (6* 7 )0 + 6 / ! " % % ,! 8& 9 ): ! 8 ,! + ! ! + 4! ! ,! ! 8 % - ! ! - ! + % 8 ! + 5 & 3+ ! 8 %% ! (5 )* 4! ! 5 # % , % # % "# , &% ; ! ! ! ! Æ! - 5 ) ! , Level k I II Level 2 III IV Level 1 Lattice boundary Frequent itemset border Chi-square border 4 ) ### " 5 + + 6 # ## ++ 6 # ## +++ 6 # ## +7 6 # ## <% # , ! - ! + ! % 5 # + = % > ! + ! % ! 4 1 1 " + ! , 8+! ! % % ! 1 )2 % % ! ! % % & % (5 ) <% % % 1 )2 ! ! % %& ! 4 1 % ' ) ? ! & ? % ! ? % # ! 8+! % # ! -- 5 ) 0 ? % % & @ ? % % - % ! % 6 % - % , % ? # A# - 8 0 % & % + -- 5 ) 5! % ! 6 8 @ - % % - % % % + + # ! ! ! % 3 ! % ! , ! / % ! , 6 6 7 ! 6 ! % ) A ,! ( * B % % ! 5 # ; C 6 D + ! 5 ! ! " ! % # ! E ' ; ( ( ( * ** ()* % ! # ,! ( * ; · · 4F! 6 % , # , ( * ! % 3 ! 5 ! % ) + % # ' ; ( * C ( * C ( * C ( * ( * ; (* 8 ! # ( * % 1 )2 ! + ! ! % % ! # <% ! % % ' ) 1 % - % ! % & % ! ! - ! % 3 &% Æ / " ! (% ) ! * + 5 # 3 ! 9 9@ + G0 ? " # ! ! + & <% , + & H ) 5 6 % , D + ! % 5 & % ? % ! E Æ D &E Æ ! ! - ! % # ! )9999 ! A 0 ( * % ' ) ½½ ) ½¼ ) ¼½ ) C C % ? % Æ $ Æ ! % ! + % % ! ' $( * (* ; % $( * ; ( * (* ( * % ) C) - % ; 9 <% ! - ; 9 % % ( * (* 6 ! ; 9 ! 5! ! - ( * (* 6 ( * ( * 6 5 ! ; () * % (* ; Æ % % ) ) ½½ ½· ·½ ; ½· ) ½· ·½ ) ·½ ; ( * ( * ; (0* , + % ' ; ( C *( C * ; ; ( * ; < , 0 ; (@* (:* , ! , 5 + Æ % + ' I I I I ; (1* I I I I % I E , ! % Æ , : ? % Æ Æ ! 89 8 898 : ; 9 : 9 0# $ Æ (G * @ @ 1 ; ) ) Æ ! > , 1 % , % % ; Æ ? % Æ % ! D & # % ' % ! % % &% # ! + ' ( * ( * ; (G* ( * % % 9 ) - % & I ! I ; (# ( ** ( * ; ) (I* ; ) # ( * % % ; ? # #6 ! I ; (# ( ** % ( * ; ) # ( * ! ' ( * ; ( * ( * C C ( * ( * ; () # ( ** ( * C C () # ( ** ( * ( * # ( * ( * ; ) # ( * ; (2* % ( * ; ) ( * ( * ; ( * A, G % % ' # ( * # ( * ; ) # ( * # # ; # ()9* , ; 5 % ! ! Æ ' # C # # # ())* # # 5 # ; (0CC0C @ 1*(9 @ 1* ; )G ; % % 5 + ! ! % " % - ! % ! (%* 5 , % ! 9= 09= , 9)= 9@= @= ( ! * % # % Æ % % 5 " % 8 %! 0.001<Support<0.3 0.5 0.5 0.5 0 −1 Correlation 1 −0.5 0 −0.5 0 0.5 Lambda Coefficient −1 1 0 −0.5 0 0.05<Support<0.3 0.5 Lambda Coefficient −1 1 0.5 0.5 0.5 −0.5 Correlation 1 0 0 −0.5 0 0.5 Lambda Coefficient 1 −1 0.5 Lambda Coefficient 1 0.05<Support<0.8 1 −1 0 0.05<Support<0.5 1 Correlation Correlation 0.01<Support<0.3 1 Correlation Correlation All Pairs 1 0 −0.5 0 0.5 Lambda Coefficient 1 −1 0 0.5 Lambda Coefficient 1 Æ 1# ! >! ( !* ! (* ; ( * ( * - ? ! ! % B ? # 5 # 3 ! % % + ( * ; ( * ( * % ! ( * ; ( * ( * / %! ! % % ,! ' ( * ; (* ( * ; (* C ( * ( * ( * ; ( * ( * ( * ()* H + ! % &% ! % % # # ' (* C ( * ( * (* ( * ( * ; ()* % Æ % 5 & % ! 6 # % - % % % ! % % 0.001<Support<0.3 0.5 0.5 0.5 0 −1 Correlation 1 −0.5 0 −0.5 0 0.5 Uncertainty −1 1 0 −0.5 0 0.05<Support<0.3 0.5 Uncertainty −1 1 0.5 0.5 0.5 −0.5 Correlation 1 0 0 −0.5 0 0.5 Uncertainty 1 −1 0.5 Uncertainty 1 0.05<Support<0.8 1 −1 0 0.05<Support<0.5 1 Correlation Correlation 0.01<Support<0.3 1 Correlation Correlation All Pairs 1 0 −0.5 0 0.5 Uncertainty 1 −1 0 0.5 Uncertainty Æ 1 - ! , # J 3 % ,! H ! ( , * - % % % ? ! ! 3 /3 )G ! ! ! 3 ! ' ) ! ; 9 ! B % ( * ; (* ( * ! ! % ( * % ! ! % (* ( ( ** % ! + ! 6 + (% + # ( ** % , + , ( (* ( ** + % % H! # + 5 # )@ ! ! ! % (* % ( * (* ( * ) + % % ! # % 3 Æ! ! + ! " 3 - % ! ! 5 # + + % / %! ! , ! , % ! ! ! ! + . % &# # #& ## ¼ ! " "= + = - ! " ; ; Support<0 or Support>0.9 1000 800 800 600 600 Count Count All Pairs 1000 400 200 0 400 200 −1 −0.5 0 0.5 Correlation 0 1 −1 1000 800 800 600 600 400 200 0 0 0.5 Correlation 1 Support<0 or Support>0.5 1000 Count Count Support<0 or Support>0.7 −0.5 400 200 −1 −0.5 0 0.5 Correlation 1 0 −1 −0.5 0 0.5 Correlation 1 # " # A % ! + 8 % % ! - % ! ! ! 5 0 @ % " ! ! + Æ ! ! D % % 5 0 % % % D ! # % ! ! , - % + ! & All Pairs Support<0.01 or Support>1 1000 300 800 250 Count Count 200 600 400 150 100 200 0 50 −1 −0.5 0 0.5 Correlation 0 1 −1 300 250 250 200 200 150 100 50 50 −1 −0.5 0 0.5 Correlation 1 150 100 0 0 0.5 Correlation Support<0.05 or Support>1 300 Count Count Support<0.03 or Support>1 −0.5 1 0 −1 −0.5 0 0.5 Correlation 1 # " % # % % ! % ! $+ % ! 1 % + ! ! % % % # # 9 : < 9 ; = 9 " $ $ % - 6 % ! % A ,! ?% 7# ! 5 ! % )9 7# ! ?% % + % @= @9= ! #$%& ; ' $()"* % 9= :1= + % ! <% ! ?% G9= / % &% 7# ! % ! ?% 1@= - % #$%& ; ' $()"* & %! + ! % # + % + : < % + ! # + ' &+($ ; #( 0.5 0.5 0.5 0 Correlation 1 −0.5 0 −0.5 0 0.5 Max(Confidence) −1 1 0 −0.5 0 0.05<Support<0.3 0.5 Max(Confidence) −1 1 0.5 0.5 0.5 −0.5 Correlation 1 0 0 −0.5 0 0.5 Max(Confidence) 1 −1 0.5 Max(Confidence) 1 0.05<Support<0.8 1 −1 0 0.05<Support<0.5 1 Correlation Correlation 0.01<Support<0.3 1 −1 ()0* 0.001<Support<0.3 1 Correlation Correlation All Pairs * 0 −0.5 0 0.5 Max(Confidence) 1 −1 0 0.5 Max(Confidence) 1 Æ $ 0# / +& 5 # )) * C ) ; (( ()@* *C # ! + - (* 4 + ! + 3 ÁË & 1 )2 : )9 + % 3 ! % % # ( * ( * ; ():* (* ( * ! B % ) + 3 - ! Æ 5 ! ( * ; ()1* - % , 0 % % % Æ ' ½½ ) ; ½· ·½ ( )* ; ; ()G* 5 % ½· ) ·½ ) - ¼· ·¼ ) H ! ) ? # , )G ' ; ; ; ()2* % ' ; (9* ! + 3 5 % , - % & 8 , + ; +($ ( ; * +($ ( ; * % % ; ( * ( * ( * 5 1 G % % % Æ ! ! # ! % 0.001<Support<0.3 0.5 0.5 0.5 0 −1 Correlation 1 −0.5 0 −0.5 0 2 Interest −1 4 0 −0.5 0 0.05<Support<0.3 2 Interest −1 4 0.5 0.5 0.5 −0.5 Correlation 1 0 0 −0.5 0 2 Interest 4 −1 2 Interest 4 0.05<Support<0.8 1 −1 0 0.05<Support<0.5 1 Correlation Correlation 0.01<Support<0.3 1 Correlation Correlation All Pairs 1 0 −0.5 0 2 Interest 4 −1 0 2 Interest 4 Æ + ? # % + K %% GG: 99@ )00: @G@:@ % Æ % 5 2 5>>%%% >?% 0.001<Support<0.3 0.5 0.5 0.5 0 −1 Correlation 1 −0.5 0 −0.5 0 0.5 IS −1 1 0 −0.5 0 0.05<Support<0.3 0.5 IS −1 1 0.5 0.5 0.5 −0.5 Correlation 1 0 0 −0.5 0 0.5 IS −1 1 0.5 IS 1 0.05<Support<0.8 1 −1 0 0.05<Support<0.5 1 Correlation Correlation 0.01<Support<0.3 1 Correlation Correlation All Pairs 1 0 −0.5 0 0.5 IS −1 1 0 0.5 IS 1 Æ Reuters−21578 Finance (Support > 0.01) Retail Data (Support > 0.001) 1 1 0.9 0.8 0.8 0.7 Correlation coefficient Correlation coefficient 0.6 0.4 0.6 0.5 0.4 0.2 0.3 0.2 0 0.1 −0.2 0 0.2 0.4 0.6 IS 0.8 1 0 0 0.2 0.4 0.6 0.8 1 IS Æ @&9;= '3( # #( " # ? % ! ! D # @ &!8E )G G D # ; ! ,$ ; (*( ( * C ( * ** C (*( ( * C ( * ** (* (* ()* ! 9 (% ! * 9 @ ( * 5 )9 % % D # ! ! D # ! %! <% ! % % % 0.001<Support<0.3 0.5 0.5 0.5 0 −1 Correlation 1 −0.5 0 −0.5 0 −1 0.2 0.4 Gini Index 0 −0.5 0 0.05<Support<0.3 −1 0.2 0.4 Gini Index 0.5 0.5 0.5 −0.5 −1 Correlation 1 0 −0.5 0 0.2 0.4 Gini Index −1 0.2 0.4 Gini Index 0.05<Support<0.8 1 0 0 0.05<Support<0.5 1 Correlation Correlation 0.01<Support<0.3 1 Correlation Correlation All Pairs 1 0 −0.5 0 0.2 0.4 Gini Index −1 0 0.2 0.4 Gini Index Æ A #$ % )G + 3 + - ; ( * (* ( * (* % 9 @ 9 @ 8 - ; 9 % ! % 5 )) 0.001<Support<0.3 0.5 0.5 0.5 0 −1 Correlation 1 −0.5 0 −0.5 −0.2 0 RI −1 0.2 0 −0.5 −0.2 0.05<Support<0.3 0 RI −1 0.2 0.5 0.5 0.5 −0.5 Correlation 1 0 0 −0.5 −0.2 0 RI 0.2 −1 0 RI 0.2 0.05<Support<0.8 1 −1 −0.2 0.05<Support<0.5 1 Correlation Correlation 0.01<Support<0.3 1 Correlation Correlation All Pairs 1 0 −0.5 −0.2 0 RI 0.2 −1 −0.2 0 RI 0.2 Æ 1*2 $ % G ! ' ; (* ( * (* ( * % %! ; ! , ( * , (* ! %! % % ( * (* ( * ! # ( * $ " + " >& % C + ) ( % ( * * 5 ) % % # Æ - % % % % ! & + # ## # ' ( ' ( # ' ( 0.001<Support<0.3 0.5 0.5 0.5 0 −1 Correlation 1 −0.5 0 −0.5 0 2 Conviction −1 4 0 −0.5 0 0.05<Support<0.3 2 Conviction −1 4 0.5 0.5 0.5 −0.5 Correlation 1 0 0 −0.5 0 2 Conviction 4 −1 2 Conviction 4 0.05<Support<0.8 1 −1 0 0.05<Support<0.5 1 Correlation Correlation 0.01<Support<0.3 1 Correlation Correlation All Pairs 1 0 −0.5 0 2 Conviction 4 −1 0 2 Conviction 4 &Æ - & ! % & ! -- 5 ) 5! % # , 0 J K 1 % , # % % ! - ! ! % !& <% ! + 3 ! - ! 3 ! ! ! % ? % % # & $ & %! & % ' ( * ( * ; (0* ( * ( * ( * 8 % % ? % , B # % # ¼ ¼ % ' ( * ( * ( * ( * ( * ( * ( * ; ( * ( * ( * ( * ( * ( * ( * ; ( * ( * ( * ( * ( * * (( * ; ( * ( * ( * ( (@* * ( * ( * ; , % + ' $ ( * ( * ; ( * ( * ; ( (* ( * * (:* + % ! 5 ! #6 " % ( * ( * ( * + + / %! ! % Æ 0 ! K- %& ! % ! <% % % Æ / %& ! % ! % ( 9 * / Æ D # ! % % % ! 6 ( * <% !! % & % ' + $ @+ A " #$ C 9D ;; ;E=9 ;= 99 ;= &; &< E=99 &< 9D ; ;E;E ;=< 9 ;=<9 9:< E=9 99 C9 9D ;9: ;E; ;=< 9 ;= :: 9 E=9= :== C 9D ;:E: ;E9 ;<E : ;<E 99 ;; E= <: C ;D ;E: =<; ==< ;; == 999 EE99 99 C9 ;D ;:E9 =< ==;E ;< ==;= ;:= 9:; EE9 ;< C ;D ;; =;< =EE ;< =E= < :<< EE9 = C D ;:9 E:9= EE= =: EE< = ;9 E= ; C9 D ;:: E: E:9: = E:99 9 =:9 E;E= E C D ;=: E E: = E:E <E; ;<9 E;;; <E9 C :D ;; E=< E:9; :9EE E:99 =< E: EE =< C9 :D ;= E= E: :9E: E::< =<E< E99 E<E == C :D ;; E=;9 E;: :;< E;9 E9; E E:9< ==E; % #! " # &Æ " ) Æ # "# " # % 8 % ! + 8 " % ! ! % % Æ % <% , ! % H! ( -8 # + K-* ! % (% !! * % ! & -- 5 ) ! % & 5! % & 5 %& % 8 % ! H 3 ? & - % # 9 @ "% ""% # 7 7 7 1# . " " 6 '# 1& ( @ "% ) +* # % "5 & 5E9FE 9EE: : @ "% ) +* # % " % " # + ! " #$ ! ! " ;F9< , " 9EE: @ "% # @ * 3 " " + ! %& '() " =;FEE " 9EE 4 G H 3# @ / # * + I B % J* 9E= < ) G. A % K 7 # A , L" # # 5 # + ,, " F< " " 9EEE ; G @ % # G# * *5 AM" + ! 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