Mining Database Structure; Or, How to Build a Data Quality Browser Tamraparni Dasu, Theodore Johnson, S. Muthukrishnan, Vladislav Shkapenyuk AT&T Labs–Research !"#"$ &% '% $(
ABSTRACT
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1.
INTRODUCTION
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5.00.
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1.1 Related Work
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2. SUMMARIZING VALUES OF A FIELD
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2.1 Set Resemblance
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2.3 Substring Resemblance
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x 86"(Vf6"("(,+-"z "zQ$("5Ff69" b5"k"#"6 ,6"("(,+-"X "f,+-+->2:A"(15FY!"#$ 092-" "% /%j6"("\C ,+-">+->'1|A"(1TC+->'1P"(1|+->'1|A"(1TCFY"#+-/MA"(1
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3. MINING DATABASE STRUCTURES
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3.1 Finding Join Paths
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º ë ¼W ^ ì ^ ígð
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3.2 Finding Composite Fields
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5.2 Estimating Join Sizes
x Z["(T["(:"(+-,"# b5"j"#2-;"j "j9+-2-+3 18F "j2-C +-"(@+-/"f*"#Q+->"W "!Fg"{"#$(1d6+-Q+-9+.4F_ " 2-"#+-8z?;"#2.6% "#"["#23&b52.679:"i6+3,$#2-@"#"(T T+-;2-231 Abz"X+-Q"6"!,+-T"\"#Q+-/7T1»_"#Q+->'+./f " +-'"5 "zFg"{"#$(1*6+-Q+-9+.$#$#'"#231% â } "W6fb5"!"6+->z"\:"\+.,"(Ti+-z"#+3+."!$#:'" 6'*b@ +-$ H$@9:"f"#2-""#64 "f92.+-$%
Error in intersection size estimation, 50 samples 0.8
Error in estimation
0.7 0.6 0.5 Error in Join Size Estimation, 100 samples
0.4 0.3
1.4
0.2
1.2
0.1 0
0.2
0.4
0.6
0.8
1
Resemblance
ÓBÔ±ÕÖT×¾ØeÙÚtÛÜÝ>Ø×Þ>ØßÝ#ÔàÜÂÞ#Ô±á8ØØ.Þ>Ý>ÔpâZã+Ý>ÔàÜ:ä:å+æ¤Þ>ãâZç è±Ø.Þé
Estimation error
1
0
0.8 0.6 0.4 0.2 0
Error in intersection size estimation, 100 samples
0
0.8
0.4
0.6
0.8
1
Resemblance
0.7
Ó ÔÕÖ5רZìÚÝ#Ôpâµã+Ý#ÔàÜ:ä ÙææëÞ>ãâZç èØÞé
0.6 Erro in estimation
0.2
0.5 0.4 0.3 0.2 0.1 0 0
0.2
0.4
0.6
0.8
1
Resemblance
Ó ÔÕÖT×¾ØëêÚ!Û/ÜÝØ×Þ>ØßÝ#Ô±àÜÂÞ#Ôá8ØØÞ>Ý#ÔpâZã.Ý#ÔàÜ*äBÙææeÞ>ãâZçHèØÞé Error in join size estimation, 250 samples 1.6 1.4 1.2 Error in estimation
I]""#"6S ",",¸¬06ç;+3ZFz?;"#2.6f 7bz"(" "6L+-| "d+."("($(+-M+-'"6P "(+-X Q+-R+-'"0F "k Q+-U+- "6 :+-Ti+- "7 ³³C,2-"# +->+-'"%[xy?;/"#zT Abz" 2- "V;6 Q"6 #³³C,2-" +-Z+-'"i/A+-Q_ " $(;2; Q+.P+-'"# '", ">6'H:+-Z+./+3?;$#231|9:"#2-b ""#;6P2.+-"%4I]" 2- "46 QQ"6L"#Q+->"#*+-B¸T% 23 / L "("0"0Q+.2-2 "(A"(2X +-/ C"(>"(Q+.>'"#>"#A"#EFg"(> "46 Q,"# z+. "(A"(1E$"Ob5"S"S92-"U|$#"($(231="#Q+->"U "U6"\4F >/+-6"fF[ "z +-H+-2.2&;$#"Z+-/ "7,"( T6 6"#$(+-9:"64+-P- #¬%z "(," bz"Z6*X"#"6d*Q"f " $(;2@2."#,F! "0,QFg"{"#,2-"(# 5+-Q"6Rbz"H$ Q"k "#+3j ; 2."##%V5"6,V"#2-# "_ Q+.,+- '2Ìd%,I|"*"#Q+->"6 "U{AC/ "("#92g$#"4+-/]{C/ +-/"(>b@+3 N³ #³³T '³ ³³T ;6*³!,2-"## 6*2-W$#,"#67 "z"($( "("#92g$#"79:"\ b5"("#0 "7;+3@F?;"#2.6#% I= "#]?;6+./H+-,+-2g'?"#2.68+-/O{AC/,# _b5"d">+-"(C "(Q"6L+.MU+-,+-2.+3 1L,"#",' "(* ;MUT,"\+.$,2-" $\ >j "k+."("($(+->+-'+.O"(u$#,"6H, "8$\;2_"("#C 92.$("'>+-d2 « Ì +-B "S³'Cy,2-"O"(:"(+-,"# @6KT# Ì +. "4 '³C,2-","(:"(+-,"#% $($#'"#231P"(Q+.>'+-/U{AC/ "("#92g$#"*+-7"+-"(7 S"#Q+->+-/d+-T"\"#$(+-P+.ÖHÞ>Ý>ØðZñàÔòÜcÞ#Ôá8ØZØ.Þ>Ý>ÔpâZã+ÝØä Ùæ+æeÞ>ãâZç è±Ø.Þé
Estimated vs. Actual Q-gram Resemblance, 50 samples 1
Estimated resemblance
1
0.8 0.6 0.4 0.2 0 0
0.2
0.4
0.6
0.8
1
Actual resemblance
Ó ÔÕÖT×¾ØCõÚ6öyóRÕ×¾ãâ÷×¾Ø.Þ>Ø.âø èã+ÜHߨ¤ØÞ>Ý#ÔòâZã+Ý#Ô±àÜ:ä|å+æCÞ>ãâµó ç èØÞé $", ">+-A"(",FX:+.92-"02-"(8+-*$ ]>2-2."\%HI|" $N$#$#"#231E"#2-2! "O6+3"("#$("U9:"( bz"#"#K2./" X,"6+-H 60>2.2"#"#*92.$#"f+./,³C,2-"7{ACy/Ð+-/;"%
5.4 Q-gram Sketches
_+-;2.231 Tb5"!"#2-;'"! "W$#$($\1>F[{AC/ A"\$\ "##%V +-["(:"(+-,"# bz"k"j "z,"5"(VF;¸A«@;+3VF?;"#2.6_ ; b5""6S+.S ",{AC/ +-/","(:"(+-,"#%*I]""#Q+->" ! " j 6+-Q$#"Z9:"( bz"#"#H "7>2.+-'"6]{AC/çA"#$(*6+-Q$#",+-*2."6]/A+.Q "W$(2&{ACy/ A"#$(X6+-Q$#"f+-H_+-/"7²8FG!³C,2." "#Q+->"(# i;6P+.M_+-/"O ³4FY4 ³C,2-">"#Q+->"##% 23C / | "O '³'C,2-"d"#Q+->"#* ;A"dU$\ P2.bz"(,"( ;U "³C,2-"*"(Q+.>'"## "*³'C,2-"*"#Q+->"#!$ "6+-231R6+-Q+-/+- E9:"(yb5"#"(R>2-2 j,"6+.H V6L2g'/"U6+-QC $#"##%7I]"$#$#2-;6"* f231P³>,2-"#7"8"{+3"6UFY {AC/~A"#$(@A"($ &% I|"8"* Z{AC/ A"#$\Z6+.Q$#"6P{AC/"#"(C 92.$#"X"k' "(z6+3"("#j6$#,2-"#,"#18,""##%_x _+-/"Z Abz"@2-V "@$(;2;{AC/ªA"#$(56+.Q$#"@/A+.Q
Q-gram vector distance vs. g-gram resemblance Estimated vs. Actual Q-gram Resemblance, 150 Samples 1.4
1 1.2 Q-gram vector distance
Estimated resemblance
0.8
0.6
0.4
1 0.8 0.6 0.4 0.2
0.2
0 0
0 0
0.2
0.4
0.6
0.8
1
Actual resemblance
Ó ÔÕÖT×¾ØùÚØ.âø èã+ÜHߨ_ØÞ>Ý#ÔpâZã.Ý#ÔàÜ:ä:Ùå+æÞ>ãâó
çHèØÞé
0.2
0.4
0.6
0.8
1
Q-gram resemblance
Ó ÔÕÖT×¾Ø}ÙÙÚIöyóRÕ+×ãâÿýØßÝà×ëðHÔÞ>Ý>ãÜHß2Øfý5ÞéóLÕ×¾ãâ Þ>Ø.âøHèãÜHß2Øé
×¾Øó
"X$(;2;{AC/ª"#"(92.$#"kFYz "!¸«W;+-jF?;"(2g6j"6 +-f "V"(+-"(:"(+-,"#% 23 / 7 +./ C"#"#*92.$#"[;+3 "7@ +./ Cy6+-Q$#"f+3# ; "(b@+-"f "("7+-k2.+32-"Z$#"(2g'C +-H9:"\ b5"("#4"#"#*92.$#"7;646+-Q$("%
Estimated vs. actual q-gram vector distance, 50 sketch samples 1.2
5.5 Qualitative Experiments
Estimated q-gram distance
1 0.8 0.6 0.4 0.2 0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
Actual q-gram vector distance
Ó ÔÕÖT×¾ØuûÚüö@óLÕ×¾ãâþýØ.ß2Ý>à×JðTÔòÞ>Ý>ãÜTߨsØÞ>Ý#Ôpâµã+Ý#ÔàÜ:ä¤å+æ Þ>ãâZç èØÞé
Estimated vs. actual q-gram vector distance, 150 sketch samples 1.2
Estimated q-gram distance
1 0.8 0.6 0.4 0.2 0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
Actual q-gram vector distance
Ó ÔÕÖT×¾ØeÙæ5Ú!ö@óLÕ×¾ãâÄýØßÝ>à×XðHÔÞ>Ý>ãÜHß2Øä(Ùå+æëÞ>ãâµç èØÞé
x a "|"#T+-O"(:"(+-,"## fbz"L ;A"|"(Q92-+- "#6` ; >2-2[,>+-"#f'",$#+-"#fFYf "*:"Fz"\2-+-/ "0Q$("4F7O2g'/"O;6M$#,2."\M6'9;"%EeWb5"#"( "Z{"#Q+-HF[b@ "( "(@ "7,>'+-"#@$(2-231H "#2-H+-4 " "(2-+-H$#"#XQ+-2.2&"#"#659:"ZQb5"\"6% } "!6'f"(zbz"!"XFGz"(:"(+-,"#j+-z$(?;6"#+.2$#:C "!6' 7bz"X$#56+-$#j1;+-$#2.k{"(1*"(23#% eWbz"#A"( Xb5"S$a6+.$(H+-K/"("(2f "S"(FG2-"#0F8 " 2-#%
5.5.1 Using Multiset Resemblance
A"(+-PFkj"#2-2.>Pb@ +.$ S ;79:"("#S"(2."#"6P0"#A"(2 "\j$#2-2."($(5;6Q"#j*23+-"(i+-/;'"#iF2-2?;"#2.6Vb@+3 H2."#QP³R6+-Q+-$\U2-"#|L"(Cy6 Q92-"|;',"("\\\% z"#2-2->,$(+-jf2FY5{"(1+-/W "k2-+-"(j+-/"( H?;6]2.2i?;"#2.68b@+3 LH,+-+-*¨u"(Q+.>'"6;W"#"(92.$#" >/+-A"(H?;"#2.6% } "7"#23!+-W6+.2.1A"64 "7"(W+-O'C 92-"Wb@ +-$\ 0+.$#2-;6"#@$#2-,5+-;6+.$#+-/ "f"#Q+->"#6>"#"(C 92.$#" A"#Q+->"6+-"("#$(+-,+."6W +-FG"#{T"#$\1 6"(:"#;6"#$#+-"## 60"#Q+->'"6* Q+-H+-;\%Vz"#2-2-> V9+-2-+3 18f{+-$T2-17;68+-T"\$(+-A"#231Z?;6
+-/ C"#"#*92.$#"k?;"#2.6j ;59:"#"#>Z6+-Q+-$\52-;92-"!FG"" 60 @2-"60"#"(2"(:"#$("606+-$#'A"(+-"##% } "\"'"+-"(y1HFi "(W,"( T6@FG!?;;6+-/f Q+-;92-" ?;"(2g6#% ©W"U,"( T6B+-0L:"(FG " +-& !9H6+-/L +-7$#$#"(9231O2.b7% "(7,"\ T6U+-f42-UFYZ?;"#2.6 b@+3 R "0,"4,"%LxyM"(2-'+-# zb5"4 A"dFG;6 ;'& +-;92-"@?;"#2.6['"#231 ;A"k "k,"k;,"76Fg"#d6 X"#A"#0 ;A"f+-,+-2.X;,"#\% ,"X +.Q+-$'"6,,"( T6*+.i7$#2-2-"#$(57'+."\ 1*FFY"'C "(dF7 "H?"#2.6 @$ =d "O6'P 1:"HF7 "H?;"(2g6 k " 2-"#/ OFi "Z?;"#2.6 "8;"*Fj "Z$\ $\"(f+-U "Z?;"#2.6
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A"U+-,+.2.'4FY"#"(H", ;6/"6BL9:"U+-,+-2g'%heWb5"(A"( +-0 1:"OF8?;2-+-/M+-H$#"#+-92."O|Fu2-"|:+3+-A"#4;6 FY2-"]"#/A'+-A"##% } "O"#KFG4 "HFu2."S:+3+-A"#0+-0"#T+3C 6"#>u"% /%,yb50?"#2.6Z,+-/ 7$#+-||C'A"(2.+-/0"( F["#2-"# "8T9:"(\%[IK "#0 "Z6'9;"Z$#+-X?FG"#"# ;6=?"#2.6# f"(2.+-,+-;'+-/RH>1BFu2-"]:+3+-A"#HH+- :+-92-"f+-k$(+3+-$2u%j;2-"f"#/A'+-A"#5$0$($#kb@ "#d8?;"(2g6,+- :2-2."6Sb@+3 P"\:"($("6U2-"## &"% /%d?;"(2g6Ub@ +-$ ]+-7C :"64,$#T+-O4 ³,6+-/+-!A"(1d,+-/ X$#T+-U"#+."(x j7$\ *Ùy"#Ú _Ù 7A"(1Ú &Ù eW,+.6 >6+-Ú "($% } "5?;"#2.6"("#, !$#+.2- T,"\+.$j6' A;67 "\"(FY"5+-[_"#"#"6 W*>$ d,8?;"#2.6db@+3 ] #³,6+-/+3X"#+-"##% ^T,",Q1Q"#,Zb@+-2.2@'"#,ZU$#2.+-Fg1L ">;'">F@ " 6T z"% /%L;," i66"## i"#2-"# "0T*9:"( ["($%= AT @'% } +-dy1:"UF7,"U"(2."($(+-A"UFY"'"O$B "#2-BL"#2-+-,+-;'" FY2-">:+3+-A"## &97+3ZQ+.2-2i"(fFg "92-"#,fFz " FG""A"($(fA$\ %7x O66+3+- "8,"( T6H+-WFg/+-2-" ÍPb5"423bk#1,"#"#äP"($#"(>O"(bÐ6'OFG>+.R "\2-+-#%JeWbz"#A"(0b5"]"O ;'H9: NF* "#"Sy1:"# Ff?;2-+-/P"0"(FG2@6 Q$(*S "0?;2-+-/S"#$ +.{"( 6+-$#"60+.0 +-@;:"\%
5.5.2 Using Q-gram Similarity
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+-/ 231OA"6H"#2-f"\"#6S91H "{AC/ÖA"($ ]{"(1 bz"("8 +-/ 2-1d"#2-"# ;9@ "Z{"(1d,+."#6H"#A"(2+-"("#QC +-/O?"#2.68"("6|91P "0{AC/ +-/;"%SI|">$#$#2-;6" ! "#"Z2-7'"*$#,2-"#,"#'1 ;;6U9: O'""\FY2+. *9b@"(%
6.
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CONCLUSIONS
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7. REFERENCES
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