problems of text mining, such as document indexing, document clustering or text ... while clustering methods organize documents into groups based on their ...
([SORULQJWKH8VHRI)X]]\6LJQDWXUHIRU7H[W0LQLQJ .RN:DL:RQJ6HQLRU0HPEHU,(((7RGVDQDL&KXPZDWDQD0HPEHU,(((DQG'RPRQNRV7LNN
Abstract²7KH FODVVLFDO DSSURDFKHV IRU WKH WUDGLWLRQDO SUREOHPVRIWH[WPLQLQJVXFKDVGRFXPHQWLQGH[LQJGRFXPHQW FOXVWHULQJ RU WH[W FODVVLILFDWLRQ UHSUHVHQW WKH WH[W DV EDJRI ZRUGV :RUGV WKH XQLWV RI WKH UHSUHVHQWDWLRQ DUH GHWHUPLQHG E\ WRNHQL]DWLRQ XVLQJ HJ ZKLWHVSDFH DQG SXQFWXDWLRQ FKDUDFWHUV DV VHSDUDWRU 7KH EDJRIZRUG EDVHG PHWKRGV IDFH SUREOHP ZLWK QRQVHJPHQWHG WH[W W\SLFDO IRU VRPH $VLDQ ODQJXDJHV VLQFH WKH WRNHQL]DWLRQ EDVHG VROXWLRQ FDQQRW EH DSSOLHGDQ\PRUHWRGHWHUPLQHWKHUHSUHVHQWDWLRQXQLWV6HYHUDO VROXWLRQV ZHUH SURSRVHG VR IDU DPRQJ WKHP IUHTXHQW PD[ VXEVWULQJ PLQLQJ LV DGRSWHG KHUH EHFDXVH RI LWV ODQJXDJH LQGHSHQGHQF\DQGIDYRXUDEOHVSHHGDQGVWRUHUHTXLUHPHQWV:H SUHVHQW LQ WKLV SDSHU D IX]]\ VLJQDWXUH EDVHG VROXWLRQ XVLQJ IUHTXHQW PD[ VXEVWULQJ IRU QRQVHJPHQWHG GRFXPHQW UHSUHVHQWDWLRQ DQG SURSRVH KRZ LW FRXOG EH DSSOLHG IRU VRPH W\SLFDOWH[WPLQLQJWDVNV:HVKRZKRZWKHIOH[LELOLW\RIIX]]\ VLJQDWXUHVFDQEHH[SORLWHGIRUWH[WPLQLQJWDVNV:LWKWKHXVH RI WKLV SURSRVHG FRQFHSW FRPSOH[ GHFLVLRQ PRGHOV LQ WH[W PLQLQJPD\EHFRQVWUXFWHGPRUHHIIHFWLYHO\LQIXWXUH
:
, ,1752'8&7,21
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
0DQXVFULSW UHFHLYHG 0D\ 'RPRQNRV 7LNN ZDV VXSSRUWHG E\ WKH$OH[DQGHUYRQ+XPEROGW)RXQGDWLRQ . : :RQJ LV ZLWK WKH 6FKRRO RI ,QIRUPDWLRQ 7HFKQRORJ\ 0XUGRFK 8QLYHUVLW\ 6RXWK 6W :$ $XVWUDOLDFRUUHVSRQGLQJDXWKRU ±SKRQH ID[HPDLONZRQJ#PXUGRFKHGXDX 7&KXPZDWDQDLVZLWKWKH6FKRRORI,QIRUPDWLRQ7HFKQRORJ\0XUGRFK 8QLYHUVLW\ 6RXWK 6W :$ $XVWUDOLD HPDLO 7FKXPZDWDQD#PXUGRFKHGXDX '7LNNLVZLWKWKH,QVWLWXWHIRU&RPSXWHU6FLHQFH+XPEROGW8QLYHULWlW ]X%HUOLQ8QWHUGHQ/LQGHQ%HUOLQ*HUPDQ\+HLVRQOHDYHIURP 'HSWRI7HOHFRPPXQLFDWLRQVDQG0HGLD,QIRUPDWLFV%XGDSHVW8QLYHUVLW\ RI7HFKQRORJ\DQG(FRQRPLFV+%XGDSHVW0DJ\DU7XGyVRNNUW +XQJDU\HPDLOVWLNN#LQIRUPDWLNKXEHUOLQGHWLNN#WPLWEPHKX
978-1-4244-8126-2/10/$26.00 ©2010 IEEE
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
EHFDXVHRIWKHPDLQIHDWXUHRILWVDELOLW\WRDVVLJQPHDQLQJIXO OLQJXLVWLF ODEHOV WR WKHIX]]\VHWV LQWKHUXOHEDVH>@6LQFH FODVVLFDO IX]]\ UXOH EDVHG V\VWHPV IDFHG WKH FXUVH RI GLPHQVLRQDOLW\ IRU PXOWLYDULDWH LQSXWV ZKHQ WKH QXPEHU RI LQSXWVH[FHHGHGDUHODWLYHO\VPDOOWKUHVKROGZKLFKQDWXUDOO\ ULVH ZLWK WKH LQFUHDVLQJ SRZHU RI FRPSXWDWLRQDO UHVRXUFHV VHYHUDO DOWHUQDWLYHV KDG EHHQ SURSRVHG DV UHPHG\ VXFK DV IX]]\ UXOH LQWHUSRODWLRQ DQG H[WUDSRODWLRQ >@±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
[ [ [ [ [ [ [ [ [ [
7
sets was introduced by Kóczy [17], where $9 N ; N , and the range of membership values was the lattice of kdimensional vectors with components in the unit interval. A further generalization of this concept is the introduction of fuzzy signatures and signature sets [14], where each vector component is possibly another nested vector as shown in Fig. 1. (DFKVLJQDWXUHFRUUHVSRQGVWRDQHVWHGYHFWRUVWUXFWXUHRU HTXLYDOHQWO\ WR D WUHH JUDSK 7KH LQWHUQDO VWUXFWXUH RI WKH VLJQDWXUH LQGLFDWHV WKH VHPDQWLF DQG ORJLFDO FRQQHFWLRQ RI VWDWH YDULDEOHV FRUUHVSRQGLQJ WR WKH OHDYHV RI WKH VLJQDWXUH JUDSK7KHIX]]\VLJQDWXUHVFDQEHGHVFULEHGDVJHQHUDOLVHG YHFWRULDO IX]]\ VHWV ZLWK SRVVLEOH UHFXUVLYH YHFWRULDO FRPSRQHQWV,WFDQEHGHQRWHGDV
$ ; 6 Q ZKHUH Q DQG Q
6 Q 6L L
6L P 6 DQG GHQRWHVWKH&DUWHVLDQSURGXFW)RUH[DPSOHa fuzzy signature AS can be given as
N DLM $6 ; DL L DL NL N DLM M D LMO O
)X]]\ VLJQDWXUH FDQ EH FRQVLGHUHG DV VSHFLDO PXOWL GLPHQVLRQDO IX]]\ GDWD 6RPH RI WKH GLPHQVLRQV DUH LQWHU UHODWHG LQ WKH VHQVH WKDW WKH\ IRUP VXEJURXS RI YDULDEOHV ZKLFKMRLQWO\GHWHUPLQHVRPHIHDWXUHRQDKLJKHUOHYHO 2QWKHH[DPSOHRI)LJ
[[ IRUPDVXEJURXSWKDW
FRUUHVSRQGV WR D KLJKHU OHYHO FRPSRXQG YDULDEOH RI
[
[[[ ZLOO WKHQ FRPELQH WRJHWKHU WR IRUP [ DQG [ [ [ [ [ LV HTXLYDOHQW RQ KLJKHU OHYHO ZLWK [ [ [ [ )LQDOO\ WKH IX]]\ VLJQDWXUH VWUXFWXUHZLOOEHFRPH [ [ [ [ LQWKHH[DPSOH
)LJ)X]]\VLJQDWXUH2QWKHOHIWWKHYHFWRUIRUPRIDIX]]\ VLJQDWXUHLVVKRZQRQWKHULJKWWKHFRUUHVSRQGLQJWUHHJUDSK
7KH UHODWLRQVKLS EHWZHHQ KLJKHU DQG ORZHU OHYHOV LV JRYHUQHG E\ D VHW RI IX]]\ DJJUHJDWLRQV 7KH UHVXOWV RI WKH SDUHQW VLJQDWXUH DW HDFK OHYHO DUH FRPSXWHG E\ DQ DSSURSULDWH DJJUHJDWLRQRIWKHLUFKLOGVLJQDWXUHV/HW D EH WKH DJJUHJDWLRQ DVVRFLDWLQJ
[ DQG [ XVHG WR GHULYH [
[ [D [ %\ UHIHUULQJ WR )LJXUH WKH DJJUHJDWLRQVIRUWKHZKROHVLJQDWXUHVWUXFWXUHZRXOGEH D D D DQG D 7KHDJJUHJDWLRQV D D D DQG D WKXV
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³*7&*7&7´ DQGDSUHGHILQHGIUHTXHQF\WKUHVKROG
,QWKHILUVWVWHSWKHIUHTXHQWVXEVWULQJVDUHGHWHUPLQHG 7R WKLV HQG QJUDP Q FKDUDFWHU VHTXHQFHV DUH H[WUDFWHG DV LQGH[ WHUPV ZLWK WKHLU IUHTXHQFLHV DQG SRVLWLRQV2QO\LQGH[WHUPVWKDWRFFXUDWOHDVWZLWKWKH SUHGHILQHGIUHTXHQF\ZLOOEHH[WUDFWHG,QGH[WHUPVDUH VRUWHG EDVHG XSRQ WKHLU IUHTXHQF\ LQ WKH LQGH[ GDWD VWUXFWXUH
,Q WKH VHFRQG VWHS WKH IUHTXHQW PD[ VXEVWULQJV DUH VHOHFWHGE\NHHSLQJRQO\WKRVHLQGH[WHUPVWKDWKDYHQR VXSHUVXEVWULQJ SDWWHUQV DPRQJ WKH LQGH[ WHUPV 7KLV VWHSUHGXFHVWKHQXPEHURIWKHLQGH[WHUPVVLJQLILFDQWO\
'XULQJ WKH FRPSXWDWLRQ LQGH[ WHUPV DUH WKH IRUP RI D IUHTXHQW VXIIL[ WUHH )67 DV VKRZQ LQ )LJ IRU RXU H[DPSOH+HUHWKHIUHTXHQWVXEVWULQJVDUH)636 ^*! 7! *7! *7&! ` DQG WKH IUHTXHQW PD[ VXEVWULQJV)06 ^7!*7&!`)06VDUHWKHQXVHG DVDVHWRILQGH[LQJWHUPVIRUDGRFXPHQt.
)LJ5HSUHVHQWDWLRQRIWKHGRFXPHQWFROOHFWLRQZLWK)06V>@
,9 '2&80(17&/$66,),&$7,2186,1*)8==@
9 &21&/86,21
>@
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
>@
% /LX :HE 'DWD 0LQLQJ ([SORULQJ +\SHUOLQNV &RQWHQWV DQG 8VDJH'DWD%HUOLQ+HLGHOEHUJ1HZ