• Nenhum resultado encontrado

Extraction of Highly Utilized Itemsets from large Transactional Databases

N/A
N/A
Protected

Academic year: 2017

Share "Extraction of Highly Utilized Itemsets from large Transactional Databases"

Copied!
5
0
0

Texto

(1)

([WUDFWLRQRI+LJKO\8WLOL]HG,WHPVHWVIURP

ODUJH7UDQVDFWLRQDO'DWDEDVHV

.0DGKDYL

Department of Computer Science and Technology

VR Siddhartha Engineering College, Vijayawada, Andhra Pradesh, India

&+1DQGD.ULVKQD

Department of Computer Science and Technology

VR Siddhartha Engineering College, Vijayawada, Andhra Pradesh, India

6DL+DUVKLWD*XWWD

Department of Computer Science and Technology

VR Siddhartha Engineering College, Vijayawada, Andhra Pradesh, India

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

.H\ZRUGV8WLOLW\0LQLQJ4XDQWLWDWLYH'DWDEDVH

,,1752'8&7,21

$VVRFLDWLRQUXOHVPLQLQJ$50>@LVRQHRIWKHPRVWZLGHO\XVHGWHFKQLTXHVLQGDWDPLQLQJDQGNQRZOHGJH GLVFRYHU\ DQG KDV PDQ\ DSSOLFDWLRQV OLNH EXVLQHVV PHGLFLQH DQG RWKHU GRPDLQV 0DNH WKH GHFLVLRQV DERXW PDUNHWLQJDFWLYLWLHVVXFKDVHJLQVXSHUPDUNHWV

'DWD PLQLQJ LV WKH H[WUDFWLRQ RI SRWHQWLDOO\ XVHIXO LQIRUPDWLRQ IURP WKH DYDLODEOH GDWD 'LVFRYHU\ RI WKH NQRZOHGJH LV WKH GDWD PLQLQJ JRDO ZKLFK LV XVHG WR SUHGLFW WKH IHDWXUH EHKDYLRU IRU WDNLQJ WKH VWUXFWXUDO GHFLVLRQV0LQLQJWKHIUHTXHQWSDWWHUQVLVDIRUPHUUHVHDUFKWRSLFLQGDWDPLQLQJ)UHTXHQWSDWWHUQPLQLQJLVWKH ILQGLQJRILQWHUHVWLQJSDWWHUQVKLGGHQLQDGDWDEDVH)UHTXHQWSDWWHUQPLQLQJGRHVQ¶WFRQVLGHUWKHSURILWIRUHDFK LWHP 7R RYHUFRPH WKLV SUREOHP ZHLJKWHG IUHTXHQW SDWWHUQ PLQLQJ >@ LV SURSRVHG :KHUH DV LQ ZHLJKWHG IUHTXHQWSDWWHUQPLQLQJGRHVQ¶WFRQVLGHUWKHTXDQWLW\RIHDFKLWHP7RRYHUFRPHWKLVSUREOHPXWLOLW\PLQLQJLV SURSRVHG 8WLOLW\ PLQLQJ FRQVLGHU WKH ERWK SURILW DQG TXDQWLW\ RI HDFK LWHP 8WLOLW\ PLQLQJ VXSSRUWV WKH TXDQWLWDWLYHGDWDEDVH

8WLOLW\ PLQLQJ ILQGV WKH PRVW YDOXDEOH IUHTXHQW LWHPVHWV 7KH 8WLOLW\ RI DQ LWHP UHIHUV WR WKH XVHUV LQWHUHVWLQJQHVV IRU LWHP 7KH PXOWLSOH RI LWHPVHWV H[WHUQDO DQG LQWHUQDO XWLOLWLHV GHILQHV LW¶V XWLOLW\ ([WHUQDO XWLOLW\LVWKHSURILWRIWKHLWHPLQWHUQDOXWLOLW\LVTXDQWLW\RIWKHLWHPSUHVHQWLQWKHWUDQVDFWLRQ)RUWKHJLYHQ XWLOLW\ WKUHVKROG LI WKH GHWHUPLQHG LWHPVHW XWLOLW\ LV JUHDWHU WKDQ WKH JLYHQ XWLOLW\ WKUHVKROG WKHQ LW LV FDOOHG SURPLVLQJLWHPVHWHOVHLWLVFDOOHGXQSURPLVLQJLWHPVHW7KHSURFHVVRIPLQLQJKLJKXWLOLW\LWHPVHWVUHTXLUHVWZR LQSXWVILUVWRQHLVWUDQVDFWLRQDOGDWDEDVHDQGVHFRQGRQHLVSURILWIRUHDFKLWHP

,,%$&.*5281'

'HILQLWLRQ,WHPVHW;XWLOLW\LQ

''DWD%DVHLVUHSUHVHQWHGE\

(2)

'HILQLWLRQ)RUWKH'GDWDEDVHWKHLWHPVHW;7UDQVDFWLRQZHLJKWHGXWLOLW\LV

7:8;

:KHQPLQLQJWKHKLJKXWLOLW\LWPVHWVIURPYHU\ODUJHWUDQVDFWLRQVWDNHVPXFKWLPHWKLVPLQLQJWLPHFDQEH UHGXFHGE\LPSOHPHQWLQJLQDSDUDOOHOHQYLURQPHQW

,,,5(/$7(':25.

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

)RUFRQVWULFWLQJWKH8SB7UHHWKHQRGHVWUXFWXUHLV

&ODVV1 ^

6WULQJQDPH

LQWFRXQW

LQWXWLOLW\

6WULQJSDUHQW

&ODVV1KOLQN

`

7KHOLQNSRLQWHULVXVHGWRUHSUHVHQWWKHODVWDSSHDUDQFHRIWKHQRGHLQ83B7UHHZKLFKKDVVDPHQRGHQDPHLQ WKHHQWU\KHDGHUWDEOH

6WHSVIRU&RQVWUXFWLRQRI83B7UHH

'DWDEDVHLVVFDQQHGRQO\WZLFHIRU&RQVWUXFWLRQRI83B7UHH

)LUVWVFDQ

)RUHDFKWUDQVDFWLRQWKHWUDQVDFWLRQXWLOLW\7XLVFRPSXWHG

$WWKHVDPHWLPHWKHWUDQVDFWLRQZHLJKWHGXWLOLW\7:8RIHDFKLWHPLVDOVRFRPSXWHG

7KHLWHPVZLWK7:8¶VOHVVWKDQWKHJLYHQWKUHVKROGWKHQWKRVHLWHPVDUHFDOOHGXQSURPLVLQJLWHPVDQG WKRVHLWHPVDUHGLVFDUGHG

)RUWKHSURPLVVLQJLWHPVFRPSXWHWKHUHWUDVDFWLRQXWLOLWLHV

7KHSURPLVLQJLWHPVDUHDUUDQJHGLQWKHGHFUHDVLQJRUGHURIWKHLU7:8¶V

6HFRQGVFDQ

(DFKWUDQVDFWLRQLVLQVHUWHGDVDEUDQFKLQWRD83B7UHH

$IWHUFRQVWUXFWLRQRI83B7UHHWKHIROORZLQJVWUDWHJLHVDUHXVHGWRUHGXFHWKHWLPHDQGWKHVHDUFKVSDFH7KH VWUDWHJLHVDUHDVIROORZV

6WUDWHJ\'LVFDUGLQJJOREDOXQSURPLVLQJLWHPV'*8

6LQFHWKHXQSURPLVLQJLWHPVGRHVQRWLQYROYHGLQWKHKLJKXWLOLW\LWHPVHWVWKHVHDUHQRWFRQVLGHULQ WKHFUHDWLRQRI*OREDO83BWUHH

(3)

6WUDWHJ\'LVFDUGLQJJOREDOQRGHXWLOLWLHV'*1

,QWKHFRQVWUXFWLRQRID*OREDO8WLOLW\SDWWHUQWUHHIRUDQRGHWKHVXFFHVVRUXWLOLWLHVDUHGHOHWHGIURPWKH FXUUHQWXWLOLW\RIWKHQRGH

6WUDWHJ\'LVFDUGLQJORFDOXQSURPLVLQJLWHPV'/8

,QWKHFRQVWUXFWLRQRIDORFDO8WLOLW\SDWWHUQWUHHWKHXQSURPLVLQJLWHPVPLQLPXPXWLOLWLHVDUHGURSSHGIURP SDWKXWLOLWLHVRISDWKV

6WUDWHJ\'HFUHDVHWKHORFDOQRGHXWLOLWLHV'/1

)RUFRQVWUXFWLRQRIDORFDO83BWUHHIRUDQ\QRGHWKHLWHP¶VPLQLPXPXWLOLWLHVRIGHVFHQGDQW¶VDUHGHFUHDVHG

7KH SVHXGRFRGHIRU83*URZWKLVDVIROORZV

0HWKRG83*URZ$[%[=

,QSXW$[DV83B7UHH%[KHDGHUWDEOHIRU$[DQG=LWHPVHW

2XWSXW3+8,¶VLQJLYHQWUHH

0HWKRG83*URZ$[%[=

)RUHYHU\FLLQ%[GR

&UHDWH3+8,3 =׫

$VVLJQ3¶VXWLOLW\ XWLOLW\RIFL¶VLQ%[

&UHDWH3¶V&3%

3ODFHORFDOLWHPVZKLFKDUHKDYLQJJUHDWHUPLQBXWLOLQ3&3%LQWR%\

,PSOHPHQW'/8

,PSOHPHQW'/1DGGEUDQFKHVWR$\

,I$\ ^`FDOO83*URZ$\%\3

(QGRIIRU

8WLOLW\ 3DWWHUQ 7UHH LV XVHG IRU PDLQWDLQLQJ WKH LQIRUPDWLRQ DERXW WKH WUDQVDFWLRQV )URP WKH 83B7UHH WKH 3+8,¶V DUH JHQHUDWHG 83B7UHH ZLOO EH UHSOLFDWHG DW HDFK SDUDOOHO QRGH DQG WKH FRUUHVSRQGLQJ WKH &3% &RQGLWLRQDO3DWWHUQ%DVHWUHHVDUHJHQHUDWHGDWHDFKQRGHIRUDOOWKHLWHPVLQWKHKHDGHUWDEOH)RUHDFKLWHPV &3%¶VWKHKLJKXWLOLW\LWHPVVHWVDUHPLQHG

7KH83B7UHHFRQVWUXFWHGDVIROORZV

(4)

,9352326('6<67(0

,QWKHSURSRVHGV\VWHPWKHPLQLQJRIKLJKO\XWLOL]HGLWHPVHWVZLOOGRQHLQSDUDOOHO+HUHWKHFRQVWUXFWLRQRI 8SBWUHH>@ ZLOO GRQH DW VHUYHU DQG WKH KLJKO\ XWLOL]HG LWHPVHWV DUH PLQHG DW HDFK SDUDOOHO QRGH IURP LWV FRQGLWLRQDO SDWWHUQ EDVH WUHH¶V7KH VWUXFWXUH RI WKH SURSRVHG VWUDWHJLHV LQFOXGHV WKUHH SKDVHV 6FDQ WKH GDWDEDVHWZLFHWRGHYHORSDZRUOGZLGH7UHHZLWKWKHXQGHUO\LQJWZRWHFKQLTXHVUHFXUVLYHO\FUHDWH3+8,V IURPZRUOGZLGH837UHH>@DQGFORVHE\837UHHVE\83*URZWKZLWKWKHWKLUGDQGIRXUWKSKLORVRSKLHVRUE\ 83*URZWKZLWKWKHODVWWZRIUDPHZRUNVDQGUHFRJQL]HUHDOKLJKXWLOLW\LWHPVHWVIURPWKHSODQRI3+8,V

4.1 The Proposed Data Structure: UP-Tree

7RIDFLOLWDWHWKHPLQLQJSHUIRUPDQFHDQGDYRLGVFDQQLQJRULJLQDOGDWDEDVHUHSHDWHGO\ZHXVHDFRPSDFWWUHH VWUXFWXUHQDPHG837UHHWRPDLQWDLQWKHLQIRUPDWLRQRIWUDQVDFWLRQVDQGKLJKXWLOLW\LWHPVHWV7ZRVWUDWHJLHV DUHDSSOLHGWRPLQLPL]HWKHRYHUHVWLPDWHGXWLOLWLHVVWRUHGLQWKHQRGHVRIJOREDO837UHH

4.1.1 The Proposed Mining Method: UP-Growth

$IWHU FRQVWUXFWLQJ D JOREDO 837UHH D JHQHUDO PHWKRG IRU JHQHUDWLQJ 3RWHQWLDO\+8,V LV WR PLQH 837UHH E\ )3 *URZWK >@ 6R PDQ\ FDQGLGDWH LWHPVHWV ZLOO EH JHQHUDWHG 7KXV ZH XVH DQRWKHU DOJRULWKP 83*URZWK E\ LPSOHPHQWLQJ WZR PRUH VWUDWHJLHV LQWR WKH IUDPHZRUN RI )3*URZWK %\ WKH VWUDWHJLHV RYHUHVWLPDWHG XWLOLWLHV RI LWHPVHWVFDQEHGHFUHDVHGDQGWKXVWKHQXPEHURI3+8,VFDQEHIXUWKHUUHGXFHG

)LJXUH$UFKLWHFWXUHRI83*URZWK

4.2 An Improved Mining Method: UP-Growth+

83*URZWK DFFRPSOLVKHV OHVV WLPH IRU H[HFXWLRQ RYHU )3*URZWK E\ XWLOL]LQJ '/8 DQG '/1 WR GLPLQLVK RYHUHVWLPDWHGXWLOLWLHVRILWHPVHWV,QDQ\FDVHWKHRYHUHVWLPDWHGXWLOLWLHVFDQEHQHDUHUWRWKHLUJHQXLQHXWLOLWLHV E\GLVSRVLQJRIWKHDVVHVVHGXWLOLWLHVWKDWDUHQHDUHUWRUHDOXWLOLWLHVRIXQSURPLVLQJWKLQJVDQGUHODWLYHKXEV,Q WKLVSDSHUZHSURSRVHDQRWKHULPSRUWDQWVWUDWHJ\QDPHG83*URZWKIRUOHVVHQLQJRYHUHYDOXDWHGXWLOLWLHVDOO WKHPRUHVXFFHVVIXOO\

(5)

,Q 83*URZWK OHDVW WKLQJ XWLOLW\ WDEOH LV XWLOL]HG WR GHFUHDVH WKH RYHUHVWLPDWHG XWLOLWLHV ,Q 83*URZWK LQVLJQLILFDQW KXE XWLOLWLHV LQ HYHU\ ZD\ DUH XWLOL]HG WR PDNH WKH HYDOXDWHG SUXQLQJ YDOXHV QHDUHU WR JHQXLQH XWLOLW\HVWLPDWLRQVRIWKHSUXQHGWKLQJVLQGDWDEDVH

9(;3(5,0(17$/(92/87,216

7KHSHUIRUPDQFHRIPLQLQJKLJKXWLOLW\LWHPVHWVLVUDSLGO\LQFUHDVHGLQWKHSDUDOOHOHQYLURQPHQWE\PLQLPL]LQJ WKH PHPRU\ VSDFH DQG WKH JHQHUDWLRQ RI XQZDQWHG FDQGLGDWH LWHPVHWV 7KH QHZ PHWKRGV ZLOO JLYH D EDWWHU SHUIRUPDQFHIRUWKHODUJH'DWDEDVHVDQGIRUWKHORZXWLOLW\WKUHVKROGV%\WKHEHORZH[SHULPHQWDOUHVXOWVWKH ,PSURYHG83*URZWKLVHIILFLHQWO\UHGXFLQJWKHH[HFXWLRQWLPH+HUHFRPSDUHWKHSHUIRUPDQFHRI83B*URZWK DQG83B*URZWKSOXVRQGDWDVHWV>@7DEOHVKRZVWKHH[HFXWLRQWLPHVRQYDULRXVPLQBVXSYDOXHVIURPWR

9,&21&/86,21

7KLV SDSHU SURSRVHV D SDUDOOHO V\VWHP ZKLFK WDNHV YHU\ OHVV WXUQDURXQG WLPH IRU PLQLQJ ODUJH XWLOLW\ LWHPVHWV&RQYHUWLQJWKHWUDQVDFWLRQVLQWR83BWUHHWZRVFDQVDUHVXIILFLHQW&RQGLWLRQDOSDWWHUQEDVHGWUHVVIRU HDFKKLJKXWLOLW\LWHPVHWLVUHSOLFDWHGDWHDFKSDUDOOHOQRGH)URPDOOWKHSDUDOOHOQRGHVZHJHWWKHKLJKXWLOLW\ LWHPVHWV:LWKWKLVZHFDQDOVRFUHDWHDODUJHV\QWKHWLFGDWDVHWV

5()(5(1&(6

>@ &+&DL$:&)X&+&KHQJDQG::.ZRQJ³0LQLQJ$VVRFLDWLRQ5XOHVZLWK:HLJKWHG,WHPV´

>@ &)$KPHG6.7DQEHHU%6-HRQJDQG<./HH³(IILFLHQW7UHH6WUXFWXUHVIRU+LJK8WLOLW\3DWWHUQ0LQLQJLQ,QFUHPHQWDO 'DWDEDVHV´

>@ $JUDZDODQG6ULNDQW³)DVW$OJRULWKPVIRU0LQLQJ$VVRFLDWLRQ5XOHV´

>@ ³$7ZR3KDVH$OJRULWKPIRU)DVW'LVFRYHU\RI+LJK8WLOLW\,WHPVHWV´<LQJ/LX:HLNHQJ/LDRDQG$ORN&KRXGKDU\ >@ 9LQFHQW67VHQJ&::X%(6KLHDQG36<X83*URZWK$Q(IILFLHQW$OJRULWKPIRU+LJK8WLOLW\,WHPVHW0LQLQJ >@ )UHTXHQWLWHPVHWPLQLQJLPSOHPHQWDWLRQVUHSRVLWRU\KWWSILPLFVKHOVLQNLIL

>@ <&/L-6<HKDQG&&&KDQJ,VRODWHGLWHPVGLVFDUGLQJVWUDWHJ\IRUGLVFRYHULQJKLJKXWLOLW\LWHPVHWV.In Data & Knowledge Engineering, Vol. 64, Issue 1, pp. 198-217, Jan., 2008.

>@ 5&KDQ4<DQJDQG<6KHQ0LQLQJKLJKXWLOLW\LWHPVHWVIn Proc. of Third IEEE Int'l Conf. on DataMining, pp. 19-26, 2003. >@ -LDZHL+DQ-LDQ3HLDQG<<LQ0LQLQJIUHTXHQWSDWWHUQVZLWKRXWFDQGLGDWHJHQHUDWLRQIn Proc. of theACM-SIGMOD Int'l Conf.

on Management of Data, pp. 1-12, 2000.

>@ +<DR+-+DPLOWRQDQG/*HQJ$XQLILHGIUDPHZRUNIRUXWLOLW\EDVHGPHDVXUHVIRUPLQLQJLWHPVHWVIn Proc. of ACM SIGKDD 2nd Workshop onUtility-Based Data Mining, pp. 28-37, USA

Referências

Documentos relacionados

'HVSLWH WKH SURPLQHQFH RI VXLFLGH DV D OHDGLQJ FDXVH RI GHDWK WKURXJKRXW PRVW FRXQWULHV RI WKH ZRUOG DQG WKH VXEVWDQWLDO HYLGHQFH VXSSRUWLQJ WKH UROH RI ELRORJLFDO IDFWRUV LQ

ÀRRGLQJ ZLWK UHJDUG WR GU\ PDWWHU DFFXPXODWLRQ DQG RWKHU JURZWK SDUDPHWHUV VWXGLHG KHUH 7KH SODQW JURZWK YDOXHV ZHUH QR GLIIHUHQW IURP WKRVH RI SODQWV ÀRRGHG LQ WKH DEVHQFH RI 1 2Q

7KH UHVXOWV RI WKLV VWXG\ VKRZ WKDW WHPSHUDWXUH EXW QRW WKH DYDLODELOLW\ RI ZDWHU PD\ EH DQ LPSRUWDQW IDFWRU UHVSRQVLEOH IRU WKH GLIIHUHQFHV LQ WKH TXDOLW\ DQG

7KH PROHFXODU EDVLV IRU WKH WUDQVSRUW RI PDQJDQHVH DFURVVPHPEUDQHVLQSODQWFHOOVLVSRRUO\XQGHUVWRRG,57 D PHPEHU RI WKH =,3 IDPLO\ LGHQWL¿HG LQ $ WKDOLDQD LV D EURDGUDQJH PHWDO

2EMHFWLYH 7KH SUHVHQW DUWLFOH FRPSDUHV %UD]LOLDQ DQG $PHULFDQ QRUPV IRU WKH ,QWHUQDWLRQDO $IIHFWLYH 3LFWXUH 6\VWHP ,$36 D VHW RI QRUPDWLYH HPRWLRQDO SKRWRJUDSKLF VOLGHV IRU

7KLV SDSHU GHVFULEHV WKH UHFRQVWUXFWLRQ RI WKH GULYHV RI D SDSHU PDFKLQH IRU WKH SUHVV DQG GU\LQJ SDUW RI WKH PDFKLQH GXULQJ -XQH DV ZHOO DV WKH H[SDQVLRQ RI WKH SDSHU PDFKLQH ZLWK

7KH HOHFWURFKHPLFDO UHGXFWLRQ RI DFWLYDWHG ROHILQV LQ QRQDTXHRXVVROYHQWVLVZHOOGRFXPHQWHGLQWKHOLWHUDWXUH ,Q WKH DEVHQFH RI D SURWRQ GRQRU WKH UHGXFWLRQ RI

7KH VWXGLHV DLPHG WR HVWDEOLVK WKH EHKDYLRU RI WKH *&amp;0,3 UHVSRQVH WRZDUGV RUJDQRFKORULQH FRPSRXQGV