Automatically Combining Ranking Heuristics for HTML Documents

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1 Automatically Combining Ranking Heuristics for HTML Documents Joaquin Rapela IBM Almaden Research Center San Jose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`BC " " &' &>R $=Ra BC( 1 $38 &83 " $72cb B2 R &A ( &$ =2\ $ OI "#bb5b " " &' &>$?H =:2 $ 3 " 7!$A & & " &$A d4 Categories and Subject Descriptors e 4 f 4 fg 38 &$A {7 = N 29 X "A #}~_ 'ƒ ` B =ƒ ˆT4 74 Š9g ZkdŒ Hm+si_o!niGt Ž s7 do6 9lCkdŒAs = =pwilrbxzy: >$ 3 "OB C &$A }.c C & Bš General Terms G?W$ 38 œb 9 & /œ D OI " &3 &$ Keywords *-,/.10Hœ9žŸž žjœd*-,/.10c ) & œl*-,/.10c ) & J &' &œ $38 &N$A3 ; & BC $ +*-,/.10+ )7 &' "œit?w$ 38CP &$ % X "A 1. INTRODUCTION J*-,/.10J )7 5 &' <&M>?W " &$A - VA& 85E " F -c &&'8$?*-,/.10 2$ 3 ( ) =2\"$ 2 6 $c OI "#bbsb " " &' &X$?B " <2$ 3 4H{7 " &' & ; 2c $:&3O $C - )7& 1$?9*,/.Z0 2$ 3 4 K! S & )N' "!= ; S =2N $> & V " "A 7 O <g 7œ7 xzœ #FJ$A % & == NC<Y> & &UFJ$?V{7$A " :! Q Permission to make digital or hard copies of part or all of this work or personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and/or a fee. WIDM 2001, Atlanta, GA, USA ACM /01/11...$12.00 R!$ 29& c ª«7 Jb 2>"$A 2 ; N = =2 9$A 92 " &O P $ g fcxzœ/r $ 2> : b '5 & 9$?<*-,/.102$ 3 X"$A 2 ; 9$ 2 =2Z3$ >&3OI$ 7 B JR!$ 2S& Z X '<$?G 2$" 3 5g# CŠ=xz4 *-,/.10 )7& - &' &< 2J $ ; 9"$A3 ; & =28& 7 $- )P &?W " &$A -& % "D7E " Fc " -% ) =2 &&' $?N*,/.Z0 2 $ 3 4 K! 1' 2C 2ŸOO $A &- $ ; &2 +R &A =2 = A œ! $638 & #F\ ' &38 1 %&3OI$ $?` A " F+ ' &J 26 $: & \ $: ' &J1R! " O $OI$ &$A d $ 9 "' 38C =2Z&3OI$ " A4 7 & #F &A & 6R! &7 - $+ " &' &&62 &±- #8 B2 &3 $A 3&! )_4 $ $C =œ 5 & & " &F>$ ""H$A& $?`R! " $ 2 A2 $c% )7& :?W " &$A (OI "?W$ 3 R!$ 5 B 1 $ PzR! " =2J $ /4 T ] 8 R!$ )cr! ZOO && =2] J $A38C 83 " $726?W$ $3 ; & 3( # &O & > " & d'f ' 3<2 ; 21& 6g# "x/ $ O $ ; & 3²$?H $A38C &= & #FJ$A3 ; & & *-,/.10 )7& &'P &4VK! ` " &' &S `$3 ; & =2-& Z9R &A =28= " 9 B2 \ $38 &83 " $726&( =26 " 8$AO &38MR! $3³ & & -274 ` = &Q[O & &$A 8 & BC &$A M S =2( $9 $=RŸ 38 7 & #F R! " N>3 # &Ṕ &' & )7 >?W " &$ R<# -& 7 # A #F $ "R &A = & =2 $ %OI?W$ 38 J2 2 &$ \ P OI "/ $`< $A Ṕ R &A =2µz &R &A L =E & #F5 "L $5 4 A /3 # &P " &' &M )7 " &$A /4L ] M & $> M = " &$ A #P BC &$A G $X $=R] V ( $A38C & #FR &A =2$A OI?W$ 3 $A PzR &A =2Z3( # #Ṕ ' &> " &$A /4 $A & & " &$ 9$?S*-,/.10]2 $ 3 SR<# 2#^_ " X " " &'P & - =2+ $Z $=R¹ BC5 &A$ & 3ºbB B2 >R! " 9#P &$ =2 $ OI #bbx " &' "`$?L Z$ & "" &$A /4 K! > &A$P # 3²&< & = & >R! &7 S?Q $A3² 92$ 3 S$A & & " &$ /4 { "" &$A Š]O J =2 R!$ )I4³{7 " &$A f\2 ; "1 &$ # 3» =2( $5b B2( <R &A $A3 ; & & X < &'P &4\{7 " &$A \¼+2 "O&" ( # $?X 8 "D OI " &3 B2 { "" &$A 1½5 $=R<<NO $ ; "3a& X &A$ & 3² 2 $NbB 2 R! " 4 K! +38& "$A ; &$ 1$?N " 7ZOBOI " 1 +O P O &&=C $ Ÿ$?X 1 $38 &13 " $726?W$ $A3 ; & & :3 # &O & " & 'F ' 3H2 " " ; =2& 1g# "x $X!O $ ; & 3¾$?_ $A38C P &= & #F($A3 ; & & 9*-,/.10 )7& X ' &œ! "A &$A ($? S3 $72(R<# -R! ; 25 B2( `2 " $ $?d> B=RŸ& - 61

2 &A$ # 3»R<&83$ &AC =2# 3$72 #bb=c $ /œ7 #F ; & 2 &$OI =2d4 2. RELATED WORK TU g ŠCx!%' Fc $% $38 &= #Fc$A3 ; & 8*,/.10\ )7& &' &-&2 " ; =2_4]K! *-,/.10 )7& &' &-C "$A3 ; & =2& 8>R &A =2-3À B29A " " &` &A$ # 3a&V =2 $bb 28 XR! " 4 K! >R! " < 9$ ' =2J $ ; >& "P " ` J 9 A g# 44& =½Cxz4 K! 8 5R $ )]2 #^_ " $A3º & g ŠCx!& ] NR! " &= $AO 3&Á=C &$A ' "F $9bB B2N! =R &A 4VÂMF & ( IR! &7 S& ' =A2J$?G& " S& Z ` A -g# A4&4& C½=x/R : "D O &$ (R<2 " X $?VOI$A ; & &# ">?W$ >$3 ; & &' &4 3. AUTOMATICALLY COMBINING HTML K!&! " &$A RANKING ; & " F2 " HEURISTICS ; X $38 &X3 $72-2 $ b B2Z 5R! &A X$?V3 & #Ṕ " &' &9 )7& " &$A 4`Ã$ > 2 "& & =2%2 " &O &$ % "?W " < $%g# x 4 Ä`Å &M <3 # #Ṕ &'! )7& 5?W " &$ -R<&&V $ ; <$OP &3&Á =2_4 Ä Å µçæ È'É 5O $C 2 5 & & 8 ' &38 $? 2 $ 3 " 79É%?W$ (E F ÆZ ZR &A Ê1Ë̵zÊÍÈ ÊÎÈ"ÏÏÏdÈ ÊCÐB 4 Ñ X & "V$? Ä Å µçæ7è É G3O #F S3( # #Ṕ ' &! )P & -?W " &$A : ' &38C ` `ÉJ` &&) #F1 & < $- NE " F Æ7ˆ 38 & / & <3O #F B`É&< & ` " "A 7=4 K! $H&> $b B2% & X$? Ê % B Ä Å ; '> )7X 2 $ 3 " 7 % "$?`E "4%K! J $ &$A 6$?8Ò ; "'( )P & AÓ&JR<# OI ""8 $\6 " Z OI #b =2 $ 2 " & $C " 8 2 $ 3 " 7 ( =\E " F4 Ä Å N " '?W & &F6 )A =2+ 2 $ 3 " 7 /?W$ ME FNÆ`R< (!$ 2 " & 9&3O && =2 ; F5! #P <$? Ä Å $ OI$ B21 $ 5$ 2 " & - OI "#bb =2 ; F 5 " =4 K! - N OI #bb =2+$ 2 " & %&9?W$ 38 &&Á =2 ; F: ; & BC F: "P C $ Ô<Õ12 "b =2 ; F] ]$ c 2\Ö $ g# =fxz4 Ã$ 2$ 3 É6 $A3Ø J$ & $ Ÿ$?92 $ 3 " 7 Ù1y8É Ô Õ É `Ú 5 " <O "?W >28 $2dÛ&4 Ä Å BS " '?W & #F8 ) =2 92 $ 3 " 7 V?W$ `E7 " F8Æ5R< >$ 2 " & (&3O && =2 ; F > & $? Ä Å $ " OI$A B2 S $ O /$ 2 " & 1Ô Õ 4VK! 5$AO 3&Á=C &$A %3 " $72J &' &= #F 1 c O +$?(OBC 3 " 1 )7& Ê 1OB# S$?G2$ 3 É B28É d; "$ ( $ X2$ 3 "$A & & " &$A +Ù1y Ä Å µçæ7è É Ô Ä Å µçæ7è É R< A " <ÉÔ<Õ`É 4 6 %$AO &3Á" :6" # " &$A ŸR<&Ÿ3 = $=RÜR! " < 1$ P 2 " & %&3O& =2 ; F Ä Å $ OI$A 25 $Z &$ Ô<ÕA48K! & $ ]&2 " & $3ÞÝ> 38 /Û N G$A& && BC &$A ]3 =CP Xg ½=x œs' &' &= ' &38 V$?7 H )>$ &$A ; "UR! UR!$8 ; "45K! " # " &$A +&92 "bb =2%& MEB4G NR< (ÉBœ_É C 2$ $A3³ 5$A & & " &$A +Ù1œÆ&>E " $A3³ "$A & & " &$A +ßà 21Ê&S 9 X$?HR! &7 4 á µ Ä Å VËØ ã ß ãä Õåæ çéècê_ë è"ì ÄXÅ µçæ7è É ç èêiëèìiã Ä Å µçæ7è É ÄXÅ µçæ7è Ä Å µçæ7è É ã K! ( & $ á &9 c= A œ_$a " X E7 " & >& +ß-œI$? µ' = )38 ; " R Ô<Õ1 2 Ä Å?W$ %2 $ 3 ( Ù14 í $ c %R< Ä Å OI " #F $ 2 " 1 62$ 3 JR<# OI : $ Ô<ÕAœ> " $ : 22 $3& B $ :$?- MEB45 J =E & & =œ & 8 8 3Þ$?< Z2#^_ " ÄXÅ µçæ È'É Ä Å µçæ7è É N& E7 &A " 7N $% J 3î$?< J ; $A & JA& 8$? 2#^_ " " 4 TU ] &= Aœ - &$ J A4 26 8" # " &$A )A $ # (3 &3 3º & JP A4 746 é Ä Å &($A3O #F 2& $ 2 " =2_œB N 7 3 $ `&< N A & N$? (2 $3& BP $ =œ 5 &$8&XP A4 œd B2Z N" # " &$A &>38D &3&Á =2%C( 4 4 K! $M&5 $%3& &3&Á ( " # " &$ /4ZÃG&A % O $C72 N 38 &d "D3O >$?G 5 A& B &$ %$?H & $ /4 3.1 Numerical Optimization Method { & á µ Ä Å >N3$' &F+2 #^_ " ; & R<# + OI "N $%Ê7œG F 7 3 ; " S$?G' B " &=d$ao 3&Á=C &$A %3 " $72!R< 38)A - 8$?S 2& = ; =2 g# A x 4%T c " 7 R!$ )R! 5 2J > G$A)Ṕ ` ; & " 5&3O & 3 &$ J$?G >$A P ï C A2 " 7`3 " $72d4 K!$ 1#<&`3$' #FJ2#^_ " ; œ á µ Ä Å BS" # doi$a& R<# \Á " $+2 " & & A46ð> J & &=SOI$A& $" R< Ä Å &A J 3 )7& A &?W$ 8&!É ñ Ù14]K!(& J "D7 3 <$ B2# &$A Z 2J&!A " F&?Q =E =4 3$ XO P & N" # &=VOI$A& N$ NR< Ä Å µçæ È'É >Ë Ä Å µçæ È œl5 2 & $? ã òhã ò Ëa ZN =E # =2_48T + &N= AœLR! 82 P bb Nó ã òhã ô ó ò Ë Ï ò Ëõ ˆ_ &XB` N "^_ & Ä Å µçæ7è É $ ; 5' &" #FZ =C " ` B Ä Å µçæ7è É!R< 1ÉÔ<Õ<É 4 4. EXPERIMENTS K! 5 & " Í ; =21& "?Ç 5 $- 93( # #Ṕ ' &9 )7& 'F ' 3 =25& 5 " 7L "D OI " &3 _= ; = =2NC!g Cxz4 4.1 Implemented HTML Ranking Heuristics K! &3O & 3 " 7 2X " &' &L 2 "D =2`?W$ 38CG$?I*-,/.10 2$" 3 4ZK! & B2 "D & %O $ " = "& 7 " =2+ 2 "D $ 7& & \R!$ 2 $" %& é c2#^_ " ZbB 2Z$? *-,/.10 2$" 3 5 B26" (1$ "" & #UFc O6 O P & - 57F OI " D < && )J$ "" & #UF ; R! " % (*-,/.10 2$" 3 5µzÃG&4BŠA 4 ' $AO &&'5&> =2% $8 "3$A 5$A33$ %R!$ 2 X 9= N $ 2& " &3& B NOI$CR " =48K! -' $AO] &&'$A 5$A33$ +R $ 2 & ' B2 2é2 $ 3 +µç A4 4 œ e ²$ %K e M ZJR! &N $33$A :R!$ 29& ]*,/.10\2$" 3 µ e ð M Ý9 SœI M $ < 4 ' "33 9$ # 3à& =2N $> =2 R $ 2 V $9' "3Sg& xz4 ÃG& B #FJ 5' 3<C 5' $ =2Z 1 7 =2J& 2 "D Ng ¼xz Implemented Field Heuristics ÃG& 2 &' &1 )*-,/.10¹2$ 3 %"$ 2 Ÿ $\ &3&QC # Fé$? E " F 2 : "D71& ] OI "&b+b 2 $? *-,/.1062$" 3 4H 9#^_ " " 7< &3& # FZ3 = <B= ; 2 $ & BC X X &3& # F ; "UR! " 1E "S 2 D =4GT 5" < "D OI " &3!R! 5 N $ 38 &&Á =21& " `O $72 " R<# %T 9Ã]' B2& =2J& ]g öxz4 ] &3O & 3 =2:,G Wøz ' & B> X N "D79& 2 ` ª ùªaú 7 5b 2$?L*-,/.10%2$" 3 œa%,i ],I ûøh &' BC> X 5b '9Š A -R $ 2X$?S*,/.Z0]2$ 3 œbz*> š 7øU üé,_ ûø( &' % - J "D78& 2 1ýBþ: 2\ý ÿ Í Ody [[ ï C 4 /4 $A3J[CO $72 " [C " 7 62

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5 Uniform vs. Manual Weights Uniform Weights Manual Weights Automatic vs. Uniform Weights Automatic Weights Uniform Weights Precision Precision Recall LlCsž y us 9lCs ŒpW ŒAk_m$#LnlpW kii E s7o;s7si n mcnbid LnwWw ) ;(s t nbigt n ilkiizˆ;(s t m %/s o=pwœ:lcnbi98dpwilr]ju Recall LlCs? Z+us ŒAnBwWw Ÿ 9lCsŒApW kii E s7o;s7si nbi nb /ok_mcno=pwœanwww ) ;s tànigtanilkii-ˆ;s t²m %Ls LlpW GiGŒAo=pQkIi>5 e &A &&A =2 KL D > &' 4X 6 ) =21 e &A &&A =2 K/ "D7G " &' &M &$=R! " L B 9 MO 7&$A _ R $X &' & ; = *-,/.10 2$ 3 =E &F+$ & 6 && )7N $2# " #F "P C =2 $ N $O&$?V 2$ 3 =œi2 " & 3 " 7X && D3O & AœM 2) "F7R!$ 2- "D7 " $3î " 1 && )7(R<& & ; ; A21"$A `2 O $ 4 6 ( N8R &A5$?> A4?W$ 9 ($ 9¼J ' &µ & KL "D7=œ K/$AO:KL D =œt Ñ & )7œð> Ñ & )7 4 K! & H$? M = " &$ $A3O & $A!& & & ' 2 & :ÃG& 4B¼4 ZpW =Œ G = =pqkii>(ã$ 9 &3$A'9 " FZ = & & N O " &$ c$? (38 7 B & #F1R &A =2% )7?W " &$A &>R!$ ( % BC $?N : $ PzR! " =2 $ " OBC =4¹K!Z "D OI " &3 8 $=R< >= 3 ' ; N) " %R< :R! " )7& 8 &' & ; "= (R &A & ; =21$ %& # &$A %$ 2% & =A2J $8OI " 38 N2 2 &$ % OI "< $ 9 5$?H $R &A & Experiment 2: Automatic Weights 6 S =22$ 3 H -! & & 5 ; M$?I S$ O!{7 P & > `$$`!C A$ $A3ÀÖ!$$8µ { "A4¼4 f74 Š M $ $38 &= #F b B2c R! &A $?< 83( # #PU &' &- )7 %?W " &$A & #P & ' =26& cãg&4hf748k! & " =2cR &A N $=R< 6& c # 2Z$ 3 1$?VKG ; - 4 YX & 92$" 3!& 1 > & BC &$A % ; "<$?G 9"$ O {7& A & 9 `$$<! $ $A3»Ö!$$Jµ { A47¼ 4 f 4 ŠA R! X$A3O =2 ` "= &Q[O & &$A %OI 38 X$?d < )7& $ 8 'P & ( $38 &= & 2R! &7 VR<# Z9 )7& 9?W " &$ 'P & ( $R &A & 4VÃG& 4B½5 $=R< ` " # S$?d ` & BC $ /4 ZpW =Œ G = =pqkii> Ã$ 8$=RÜ = & > & : $A38 &1R &A OI?W$ 3 ; " " Z B é + #?W$ 3 R &A 4 { é " 1 B #F $$) $A #F J : $AO Š ] )A =2é2$ 3 4 K! 92 $ 3 " 7 $ OI$A 28 $5 ` &$=R &I " &$A J$?_ "= &Q[O & &$A : A4VK! "?W$ > > $38 &XR &A S&3-P O $C - -O & &$A 2$ 3 5$A33$ #F "D3& 2 ; F % & 5 4 K! ]2 $ 3 J 2 E7 " & 1 =2 $bb B2 :R! &A :C 2 #^_ " $A3 2$ 3 8 B2 E7 " & J =2 & % "P *N W øç zƒ > B C = ~ W # K!# & 74 Š Š 4 Š¼Š 4 f ö " 4 A ö 4 faf¼ KL$O:KL "D7 74& =faf 4 A A½ e & &&A =2%KL D & /KL "D7 74 ŠA½A½ 4 ¼fA½ T Ñ & )7 74 ½A½¼ 4 ŠC¼ ð> Ñ & )7 4 ¼Af Ž n +ª Z /ok_mcno=pwœanwww )¹j ki GiGt«;s %jukl6tgpe s7lcs ido tlkdœ Hm+si_o 35 kkiww Hmci &%Lkt; o&%lsõilnim+s kbjjo&%ls %Ls LlpW opwœ nbigtaœakiww HmciG jz*b1 nbilt± ¹ &%Lkt; o&%/s ;spqrf%do j ³ qds ŒC5S y5g1z5 Cµ * rkbl )O³ qds ŒC5- y5g1z5gj+µ9nigt n+%/kdk ¾ GwQo=p 4³ qds ŒC5\ y5g1z5g1+µnlcs D#Vs w )+5 =Q[CO & &$A & &$A d4 K! " Aœ X " # $A3ÜÃG& 4I½ & B2 < BV ` $A38C &X3 " $72&! ; & ` $5 " ""!R! " BCL #G& NOI "?W$ 38 " M&3O $C "3 B?W$ HE7 " & L $L$A P 2 " 2Ÿ2 & 8 & & 6 &$A d4ÿk!&-b " " &' &:$? ` $A38C &`3 $72( $5 " &Á" ` $N R E " B22$P 3 " 7 >5R<38) "9 $A38C &= & #F6R &A =2c )7&?W " &$ ($?B " & B M $A Ṕ R &A =2N$A " OBC =4 4.6 Experiment 3: Encyclopaedia Britannica ] =2> 2 $ 3 $3õ F"$OB =2<ÂM # &=Nµ { A4 versus Yahoo ¼4 f74 = ( B2+?Q $A3º ( & & 1 "$?S $ O ({ & & X$$! "A$ $3²Ö!$$%µ {7 A4 ¼4 f74 Š S $bb 28 >R! &7 <$?G 3 # &Ṕ &' &- ) & %?W " &$A & && ' 2\& \ÃG&4Hf 4+K! R! " G?W$A B25?W$ V2$ 3 $3¾ "F &$OB 2>ÂM # &= 2?W$ <2$ 3 $A3àÖ $$C X $CR< 8& - < "$A B28 B2 # 2J$A & 3 S$?VKG ; & - 9 OI "" & #F4 =Œ G = Ã$ 2 $ 3 $3¾ "F &$AO =2 XÂM # &= J && )7 &' &œ<ð> Ñ & )7- B2T Ñ )7œM " & =2] & '8R! " œ`r< " 12$ 3 $A3 Ö $$6 F "A =2 &$CRÌR! &7 4 Z $ =2 & { "A4S¼4 f74 œ52 $ $3Ø V "F &$AO =2 Q:ÂV & 1$A ]Z ; $?S$ 7 " 7 R<# :FOI "D7<& ) < $- 2:2$ 3 S % 5 3 N=C P 65

6 "A$ F49K!&93 = < BC9&& )7> &' &œ ; F%$ 2 " & J "$A N$?< && ) 262$" 3 œ_r<&v " ca& B ; &?W$ 38P &$ c?w$ 5 )7& JO $" N 2dœ_ 7 œ_ "F% $A 2 " & C A %R! " 4éð> Z$ " 8 2 Aœ!2$ 3 $3 Ö $$ C ZOI$$ #F\& ) =26 $:$ " 2 $ 3 " 7 N& 2 JÖ $$+ $: && ) ' &œ $A #F"$A 2 " && )7M $N$ "!2$ 3 & Q2 3 ($ O œ_r<& & ; ($?M& 5 &O?W$ 9 )7& O $ 4 R! Z3 &$A 2\& { $ Ÿ¼ 4 f 4& Aœ<2 $ 3 " $3 V "F7P "$OB =25ÂM # &=5C S' " =2(& ( S 3 R!F- # E7 &A " 7J& %OBOI " J " &$A é$?5 % "F &$AOI =2 ˆ9 "F B #F' VR<& 8 & 7 $72 " &$ - $N> $AO&Aœ&V?W$&$=R<S52 "P A &$AO3 " 7> 21 "F1$A & B2 R<# & )7X $8 =2 && 4 K!&N "O N ]&3OI$ N2 #^_ " " -$A3O =2 $1' P 2 2 R! ; 2$ 3 > BC5 &#F+ 338 &Á # 5"$A & : N& # HO O4>K!&92 #^_ " " (&X B " 2 & % R &A 8?W$A B2 ; F\ $A38C &:3 " $72_4¾Ã$ Z2$ 3?Q $A3 Ö $$œvr< " 8 "D7-& \ J& # <OBC O- 338CP &Á : %$A 8$?5 :2 $ 3 =œm :KL$OéKL "D78 &' & " & =2 `&A '!R &A & œ7r< " =M?W$ `2 $ 3 " $3 F"$OB =25ÂM # &=7œR< "!!& # OB OV P &&F1$A 1 $72 " $ F138C " Çœ NKL$AO:K/ "D7S & =21 &$=R R! &A=4 >$ 3 $3Þ V "F &$AOB =2 ÂM # &= 2$: $($A 3 b 2ˆ 7 œ` c $38 &63 $72é & =2 Á $ R &A` $( &' 4 K! ZÁ" " $:R! &A($?< e &&A =2\KL "D7 " &' &Z& ; $ "$ OI$ N O " SO $ ; "3a$?/ > $38 &`3 " $72- BC R<& & ; N2 & =2Z :{ " &$ :½ Experiment 4: Single versus Multiple Root 6 5 =2J N2$" $3³ 9 & "X$?H 5"$ O Categories from Yahoo {7& A& 9 `$$X!C A$ $A3»Ö!$$1µ {7 A47¼ 4 f74 ŠA S 28?Q $A3a "$ O S$? # &O& 5 X$$`! "A$ & $3²Ö!$$Jµ { 4¼ 4 f 4 f $%b B2c R! &A ($?S 83( # #PU &' &- )7 %?W " &$A & && ' C =2J& JÃG&4f 4VK! `R 2-?W$ <$ OI$ -{7 P & 5 X$$`! $ F1 2 & &O > X$$X! $ & X 9 $CR< & %"$A & 3 <f- 2Z¼-$?H ; & NKG ; & - A4 ZpW =Œ G = =pqkii> é " 2 $ 3 " 7 Z$C " 2 #^_ " 1 $O& # & >b 2S$?H *-,/.10+2$ 3 S ; " " <$ P " 7 2& " &3& BC $ V B -R< 82$" 3 $C " V =2- $OP &4 $ 2& &FœH J $38 &3 " $72] &A =2\:&A " R &AV $9 "5 B2( $9 <K!# < &' &?W$ V S"$ O # O & Z `$$-! $ & -?Q $A3ØÖ!$$% B 6?W$ J"$ O {7& A & 5 `$$>! "A$ $3ÜÖ $$Z4 8 $ 2 & é{ "A4!¼ 4 f74 f2$ 3 $A3 %$ O Z{ & A & `$$S! $ $3ÀÖ $$N B >5$A33$ ï C A$A JR< " 2 $ 3 " 7 & - S"$ O # O& X `$$!! $ &?Q $A3àÖ!CP $$X 2 #^_ " LA$= ; F4GK! " V O& N "D7L $A Q2 ; 6 ; " %$ :2& " &3& BC $ :& é +$ O # &O& `$$S! $ &!?Q $A3àÖ!$$5 B - <$ O S{7& A & ` X$$!C A$ $3ÞÖ = J ; =O =2 ; F N $A38 &53 " $72Z BC` &A =2 & " `R! &7` $ 9,_ ûø &' Z& \ Z"$ O # &O& Z X$$8! "A$ &?Q $A3 Ö $$ B & $ O N{7 A & `$$5! $ $3 Ö $$4 Ö $$>2$ H $ & " 2 V R!$>2$ 3 $3¾ M 3 # S& Z & A & -=C A$ Fdˆ/ 7 œ_=c A$ "?Q $A3 Ö $$JR<& & $A & 2$" 3 $3a2 &^_ M # 4M $ 2 5 BV S38 ï $ P # F6$?S 8F OI " "D7N && )7C Z& " && )7œ && )7 ; " R OBA <$?L X 3 9 # Aœ#S&S = $ B ; & 9 $( "D OI S BS2$ P 3 & Z & A & 9=C A$ FZ$?LÖ $$R<&& ; >OI$$ #FJ&& ) =2- $ $ " H2 $ 3 " 7 d& 9 V 3 =C A$ F4 K!7 œ= V38 ï $ #UF5$? S && $3»52 $ 3 " 7 & -Ö $$> $N $!2 $ 3 & Ö $$5R<& &I$ ; "UR! J2 $ 3 & J2#^_ " M= $ & 4! "A$ & S& `$ O # &O& ` X$$<! "A$ & S?Q $A3àÖ!CP $$1$C " (2#^_ " 5 $O&4ZK!7 œg#n& &&) #F: (%2$P 3 " 7N& $ 8= "A$ FcR<&S && ) $ :2$" 3 & $ =C A$ F4cð> 6 8$ " ( Q2 Aœ =C A$ "-& ] $ O { & P A & J X$$!C A$ $3ºÖ!$$:$C " 2 $O&( 26# &>O $ ; ; & N B>82$ 3 $A3 $A ( $ F%R<& &H& )Z $ :2$" 3 N& $ " = $ F4%K! " AœM2 $ 3 5& N$ O 9{7 A & X$$N! "A$ $A3ÜÖ $$8$ & :3$ && )7 $6$ " Z2$ 3 -& 1 3 %$ O 8 Ÿ $ O # &O& X$$N! "A$ & $A3 Ö!$$ 4>K!&X?W & " " =28& Z$ & 3 f( B2¼$?HKL ; & XR< " X XR! " & =25 $` & ) / &' "H M =C " G?W$ G $ O H{ & P A & X X$$<! "A$ F8?Q $A3àÖ!$$N B X"$ O & &O `$$>! $ & $A3³Ö $$4 A& /œi (Á" " $R! &A5$? e &A&7 2+K/ "D7> &' && ; $ "$ OI$ 9 O M9O $ ; & 3à$?_ ` $A38C <3 " $72 BCSR<& ; 52& =21& { "" &$A ½4 5. PROBLEMS WITH THE ALGORITHM K! X FOR &$ # B2 9R! &7 $?/3 FINDING WEIGHTS# #Ṕ &' S )7&?W " &$ Nµ { 4BfA $AO &3&Á S 5 ; &# FZ$?L 9 )7 P &$A 1 $(38 Z 52$ 3 SO?W " 9 &$ 6Ô<ÕA4MK!&<& -O "& $ $A O=4SK! &A$ # 3 `$AO &3Á" - NO "#P &$A 8$?_ < )7& 5?W " &$ - OI "M $N `2$ 3 MO "?W P "QC &$A /4N ` =&H> $ 5&3OI$ X " " &' &-$? )7?W " &$A > BC>&9 $ ; " 8$A Q2 " =2 ; F1 $AO #P 3&Á= &$ : &A$ # 3%4 KL$XOO C M V$ =E " L$?$AO &3&Á& <O & &$A (R<# P $A $A 2 " & 9 "= & $A Q2 " M>$ & $ $?G A 52 $ 3 2c E " FJR< ½ 2$ 3 < N & < $- NE " F4 3 - R $ )7& : &' &œ e J B2 e Š74 e & `2$" 3 S& Z " OI$A 5 $ 5E F1 B2 e ŠN ½7 +2 $ 3 " 7 R< " +2$ 3 - )A =2 : $ é¼ & S $ 9E " Fœ2 $ 3 M )A =2%½ &`# & ` B2 2$" 3 8 ) =2 ½7 c&z & =4 %38CD&3( 3 $$ 2#P BC &$A & e +& "138D &3 3 O "& $ À 4 B2é &$=R = & < ô ½ 1 2 e Š& 9 &3$A'5OI?W "9O & &$A ]½ ô ½7 238D &3 3õ = &L A4 4VK! " Aœ e ŠX BV$O &3&Á ; $ O "& $ % B2- = _OI 3 ; "! B e ` B $AO 3&Á " O "& $ %R<& & N& 7& -&$=R =&Ç4 e ; F )7& 5 & S2 $ 3 " 7 V& " M B 8 $A Pz & $A OI?W " #F38C `2$ 3 O "?W < &$ +Ô<Õ R<& & e Š5 BS )7` $ Z & `2 $ 3 ;?W$ N & "P >$ 2$ "> $9OI " #F%38C ]Ô<Õ4>K!7 œb ; &#UF:$? 5 )7& -?W " &$ % $J38C Z N2$" 3 `O " P &$A JR<& ; >$O &3&Á =2R< e Š5&S $S =28& J X )7&?W " &$ /4cK! J$AO 3&Á=C &$A &A$ # 3 ; Fc$A &F]$A Q2 " & (O " &$ c$? N )7 " &$A +92& = 2 & Z ; P " ` " &' &A4 66

7 K!&5O $ ; & 3 = ; ( $A& =2 ; F:$3 ; & 8 $AO &3ÁP &$ " # " &$A 8>3 = S$?I SO "& $ $?I! )7& X?W "P &$ NR<# S3 = $? # / = &z4l ] V V " 7 #F92 "$O& %$AO &3Á &$A % & $ %R<# Z " 5 " &' "4 TU % 2 " " ; =2: "D OI " &3 µ {7 A4¼ < e &A&7 2:KL "D7 &' &5 & 21Á $-R! &A ; = N#SRS` 5 " `O "P " Z$?> &! 8 &' & B2dœH 7 œv J $38 &J3 " $72 3& 3&Á 2Z# SR! &A=4 6. SUMMARY $A38C &:3 " $72\?W$ J$3 ; & c "A >'F ' 3:g# "x R!XOO && =2J $ 9O $ ; & 3³$?H$A3 ; & & ( )7 &' & & $`3 # #Ṕ &' )7 " &$A /?W$ *-,/.1082$ 3 4 K! X3 $72RS =2 $5bB B2 SR! &A V?W$!3 # #Ṕ &' )7&?W " &$A S' " =2Z<R &A =21= A >$?G )P & ( &' &4M D OI " &3 V & N ] ; 25R! 92 " &$AOI =2 $ A & B 9 9OI 38 5$?H 5 $A38C 53 $72d B #FX$A ' " 25 5& # & #F9$ "L "L$?7R! <N3 # &Ṕ &' &S )7& $ /4H 6 X$3OBC =2 < "P &Q[O "& $ :OI "?W$ 38 9$?G J& 7 # A #F-R! &7 2Z " ] $A Ṕ R &A =2 3( # #Ṕ ' &% )7& $ /4àK! :& P # A #F:R! &A =2?W " &$A coi "?W$ 3 =2:R!$ ( B $A P R &A =2"$A " O $CR<& > BC = S3( ' ; M) R< "$A3 ; & & *,/.10 )7& ( &' "4 YX & =Q[CO & &$A & BC $ JR! $=R! 2é 1 P $38 &= #FR &A =2\3 # #Ṕ &' 8 )7 " &$A \OI " 3 ; " " J B $A PzR &A =2 3 # &Ṕ &' &: " &$A /4 $ & "" &$A Z$?*-,/.102 $ 3 " 7 -R<# 2#^_ " J " " P &' &R! " J =2+ $%bb B2+ -R! " (?W$ ( 83 # #Ṕ &' )7& " &$A /4J ] $=R! =26 N?W$ ( \2$ 3 5$A #P & $ J < & " =2R! &7 VR! " `& &$ =2 $NOBC " P " " &' &>$?H =%"$A & & " &$A d4 O $ ; & 3 & \ 1 &A$ & 3 =2 $cb B2] ZR! &A -R! 2 " " 2% 21 $ &$A %&` #F ; & 2 "$OI =2d4 g öcxn 4 e 38 /4 J "D OI " &3 _' B27FJ$?G?W" $ 3OI$ <& %2 $ 3! )7& 4TU 4! =ƒ ü W ( GþL. ~ I º>I»XœO 5 = Aö&ÁB Af œd & œtu #Fœ_ = Aö74 g =x # / &' &5'F ' 3³ 2Z& 1 92 " ; =2 "D OI " &3 4 X 3 Ä½Å Å Æ Æ Æ ÇXš Š È\É] Cš tåtë& XÌ X XÌ Å X XÍ3 Š Ì Ž Î CŒ74 g CxÃÏ4 4 Ð5 & & ; " 4 $ &C & 9 $A <& %7F OI " && )A =2 7 # $ 3 =47T 7 S ' =ƒ ( "Ñ> W KG` A GþL.+š ~ W "ƒ" øu "GX ( œoa " öaöa &Á7öA A 7œ/{ 1à & $œi! &#?W$ œzï F = A 74 g Cx Ñ 4 HA 4IK! 5O " )Z#C $ 1 )7 y ; & A& $ 2 ` $( >R ; 4T 7 S ' =ƒ ü W ( fg9~ I~ÓÒ A.6 øç W Gz8 zƒ ~I =ƒ" z ø b " fi & " - øç z ~Iƒ" Bƒ œ/ = A 4 g# = Cx 4 à 4B G$ " =4 1 &A$ # 3³?W$ > ±-DJ' OO& 4TU S 3 ¼$? AœOBA 5 =f Á =f œzïa #F+ = A 4 & ; & N 7 Ody [A[$OI /4 3( =C=4 "$A3J[2 &$OI " [2 $[OI$ " ' 3%4 3z4 g# A x5 ¾4 e 4 œbâx4 G4BÃG " FœB{_4 4K/ )$ & )7Fœ B2J õ4 K>4 Ø " & 4FÑ9 8 zƒ A F»` ƒ" 2¾H4I!3 ; 2 A Y> & &UFZ œ/ = A4 g# CŠ=x <4 & A & Aœ 4 Ñ &$CF2_œ B2 Ñ 4 4 >$CR A4 ébc<x( OI$AOOFJ3$A (R! ; O Ù%T 4! =ƒ ü W I øu I øç z I A >ž1 &ü]žz zü :ž% DÜ ¾V D = Bƒ œboba faöa &Á7fA A 7œdÂV ; Aœ ' 7œ O &V A A 74 g# =fcx({_4 Ð-4 4 6$A - B28Ö4 Ö4 Ö $4+Ý> F?W$ 3( &$ %& & = < " & /3$72 &4T ßÞ7 I G bgz8 zƒ ~I =ƒ" ø f zi & øç z 7»` øç ¼ A œ$a & 3 >¼ 9$?zàœ OB `faf¼ Á7f¼ œh = A 4 7. REFERENCES g& xnâx4 K>4I &ÇœdÝ(4 ¾4B $ &Çœ_ 2Z N4 ¾4BÂM & "R54 $A38C >$A3 ; & BC $ 1$? 3 # &O & > ) 28 " & 'F ' 34 T 7 S ' =ƒ ü W ( ~A ƒ" z ¹I øu ø"º! 7I & " - øç z 6»< øç ¼ A œb > ; && /œtu "Q B2_œ/ A ¼ 4 g Š=x 4B & " =œ e 4 9 œi{i4 {_4 &3%œ B28 ¾4 4 R' 2 FJ$A Z & 7 3 _' "! $3O $C " & Ç4BTU 4! =ƒ ü W f < ¼ 6I > ¾V D = Bƒ (,I = A " (G` øç À ƒ" z ¹I øu Iƒ œob ¼ ö Á¼ A 7œH = A 4 g fcx 2 & &$A :$?H =C PU " A& NR ; Ṕ OA 9 )7& 3 4 & ; & N< N{7 = % & 9 C JR! ; # 5 O/y [A[C = A& RS /4 $3J[C )I4 7 3%4 g ¼x9 ¾4 ÂX4Bà ) "< B2Z 4Â! Á=PzÖ 4¹I & - øç z»< øç ¼ ẽâ ǿ ~øç ƒ"øç - IüSGX 4 H " "P e &ÇœL A AŠ74 g ½=x Ñ 4BÝ> 38 /47 é<&< $<R<`& 1' &' &4ITU,/ ~ǿ øç W øç zƒ" z œb$ 3 NŠö7œBOA "X 7 Á = œg = A 74 67

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