María del Rosar io Bruer a. I BM Scholar s Pr ogram. Pregunt as y respuest as

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1 Dat a Mining María del Rosar io Bruer a I BM Scholar s Pr ogram Pregunt as y respuest as Pr egunt as: &XiOHVHOYDORUGHORVFOLHQWHV" &XiOHV VRQ ORV FOLHQWHV TXH WLHQHQ PD\RU SUREDELOLGDGGHGHVHUWDU" &XiOHV VRQ ORV SURGXFWRV TXH VH YHQGHQ HQ IRUPDFRQMXQWD"«Respuest as: (VWiQHQORVGDWRVGHOXVXDULR 6HQHFHVLWDQKHUUDPLHQWDVHVSHFLDOHVSDUD HQFRQWUDUODV

2 Business Int elligenc e S (V XQ SDUDJXDV EDMR HO TXH VH LQFOX\H XQ FRQMXQWR GH FRQFHSWRV \ PHWRGRORJtDVFX\DPLVLyQFRQVLVWHHQ PHMRUDU HO SURFHVR GH WRPD GH GHFLVLRQHVHQORVQHJRFLRVEDViQGRVH HQ KHFKRV \ VLVWHPDV TXH WUDEDMDQ FRQKHFKRVµ +RZDUG'UHVQHU *DUWQHU*URXS B.I.: rec ursos y herram ient as S)XHQWHV GH GDWRV ZDUHKRXVHV GDWDPDUWVHWF S+HUUDPLHQWDV GH DGPLQLVWUDFLyQ GH GDWRV S+HUUDPLHQWDV GH H[WUDFFLyQ \ FRQVXOWD S+HUUDPLHQWDVGHPRGHOL]DFLyQ'DWD 0LQLQJ

3 Qué es Dat a Mining? (1997) 'DWD 0LQLQJ es el pr oceso de explor ación y análisis - de maner a aut omát ica o semiaut omát ica - de los dat os par a obt ener pat r ones signif icat ivos y r eglas de negocio. 0LFKDHO%HUU\*RUGRQ/LQRII 'DWD0LQLQJIRUPDUNHWLQJVDOHV DQGFXVWRPHUVXSSRUW :LOH\86$ Reflex iones (2000) S QRV JXVWD OD QRFLyQ GH TXH ORV SDWURQHV GHEHQVHUVLJQLILFDWLYRV«S 6L KD\DOJR TXH UHFKD]DPRV HV OD IUDVH SRU PHGLRV DXWRPiWLFRV R VHPLDXWRPiWLFRVµ QR SRUTXH QR VHD FLHUWR VLQ DXWRPDWL]DFLyQ HV LPSRVLEOH PLQDU JUDQGHV FDQWLGDGHV GH GDWRV VLQR SRUTXH HQWHQGHPRV TXH VH KD SXHVWR GHPDVLDGR pqidvlv HQ OD DXWRPDWL]DFLyQ \ QR VXILFLHQWH HQ ODV HWDSDV GH H[SORUDFLyQ \ DQiOLVLV S 'DWD0LQLQJHVXQSURFHVR! "$# %'&( # ) * %+,- /

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6 Fuente: Mining your Own Business Data Using DB2 Intelligent Miner for Data Et apas en el proc eso de Dat a Mining,GHQWLILFDUHOSUREOHPDGHQHJRFLR 7UDQVIRUPDU ORV GDWRV HQ LQIRUPDFLyQ $FWXDUDSDUWLUGHORVUHVXOWDGRV 0HGLUORVUHVXOWDGRVGHODVDFFLRQHV

7 The Mining Pr ocess Fuente: Mining your Own Business Data Using DB2 Intelligent Miner for Data El Analist a de Dat os S(V HO YtQFXOR HQWUH ODV iuhdv GH WHFQRORJtD LQIRUPiWLFD \ ODV iuhdv GH QHJRFLRV S7UDGXFH ORV UHTXHULPLHQWRV GH LQIRUPDFLyQHQSUHJXQWDVDSURSLDGDVSDUD VX DQiOLVLV FRQ ODV KHUUDPLHQWDV GH PLQHUtD S5HDOLPHQWDHO'DWD:DUHKRXVHGHOD FRPSDxtDFRQQXHYRVFULWHULRVGHGDWD FOHDQLQJ\GDWDYDOLGDWLRQ

8 El Analist a de Dat os 7HFQRORJtD LQIRUPiWLFD 8VXDULRV GHQHJRFLR El Analist a de Dat os 78 96:;< 9 9>=?@A 9 B6@ 96C D: 9E?F<G H ];?^MA <[6=< D: 9E?F<G H \ ; 96:=K I 9 D@ D: 9E?F<G H H 96: 9 D@ A:;= D@ J@G <K?8 9< D@ ;= 9 ST?UGTV>@ IW:?U; LM:;6: ;=ND@

9 Habilidades requeridas S'DWDPDQLSXODWLRQ64/ S&RQRFLPLHQWRGHODVWpFQLFDVGH PLQHUtD\DQiOLVLVH[SORUDWRULR S+DELOLGDG GH FRPXQLFDFLyQ LQWHUSUHWDFLyQGHORVSUREOHPDVGH QHJRFLR S&UHDWLYLGDG Dat a Mining Team Fuente: Mining your Own Business Data Using DB2 Intelligent Miner for Data

10 Cost os de proyec t o Fuente: Mining your Own Business Data Using DB2 Intelligent Miner for Data Origen de los dat os S%DVHVGH'DWRV5HODFLRQDOHV S'DWD:DUHKRXVHV S'DWD0DUWVDQG2/$3 S2WURVIRUPDWRV([FHODUFKLYRV $6&,,HQFXHVWDVGDWRVFHQVDOHV HWF

11 Tipos de fuent es de dat os S7UDQVDFFLRQDOHVHMODVRSHUDFLRQHV UHDOL]DGDVFRQWDUMHWDGHFUpGLWR S5HODFLRQDOHVHMODHVWUXFWXUDGH ORVSURGXFWRVTXHRIUHFHHO%DQFR S'HPRJUiILFRVHMFDUDFWHUtVWLFDV GHOJUXSRIDPLOLDU La form a de los dat os para Dat a Mining S6HRUJDQL]DQHQIRUPDGHXQDWDEOD SODQD FRPSXHVWD SRU ILODV \ FROXPQDV S/DV )LODV XQLGDG GH DQiOLVLV3RU HMHPSORXQDFXHQWDXQWLFNHW S/DV FROXPQDV ORV DWULEXWRV GH FDGD XQLGDG GH DQiOLVLV3RU HMHPSOR IUHFXHQFLDGHXVRGHODWDUMHWDGH FUpGLWR

12 Carac t eríst ic as de las t ablas de dat os para Dat a Mining S7RGRVORVGDWRVGHEHQHVWDUHQXQDVROD WDEODR YLVWDµGHOD%DVHGH'DWRV S&DGD ILOD GHEH FRUUHVSRQGHU D XQD LQVWDQFLDUHOHYDQWHDOQHJRFLR S/DV &ROXPQDV VLQ YDULDELOLGDG GHEHQ VHU LJQRUDGDV S/DV &ROXPQDV FRQ YDORUHV ~QLFRV SDUD FDGD FDVR GHEHQ VHU LJQRUDGDV 1UR GH FXHQWD La c alidad de los dat os (O p[lwr GH ODV DFWLYLGDGHV GH Dat a Mining VH UHODFLRQD GLUHFWDPHQWH FRQ OD CALI DADGHORVGDWRV 6H GHEH LGHQWLILFDU ORV GDWRV IDOWDQWHV missings RIXHUDGHUDQJR out lier s

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14 Preparac ión de los dat os `ba cta dea f$ghi jklg m gn go$ctgp `ba cta 7UDQVIRUPHG'DWD ([WUDFWHG,QIRUPDWLRQ $VVLPLODWHG,QIRUPDWLRQ 6HOHFW 7UDQVIRUP 0LQH $VVLPLODWH Dat a Warehouse S'DWD :DUHKRXVH LV D VXEMHFWRULHQWHG LQWHJUDWHG WLPHYDULDQW QRQ YRODWLOH FROOHFWLRQ RI GDWD LQ VXSSRUW RI PDQDJHPHQWGHFLVLRQV %LOO,QPRQ S$FRS\RIWUDQVDFWLRQGDWDVSHFLILFDOO\ VWUXFWXUHGIRUTXHU\DQGDQDO\VLV 5DOSK.LPEDOO

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17 OLAP S+HUUDPLHQWDV~WLOHV\SRGHURVDV SDUDDFFHGHUD%DVHVGH'DWRV\ 'DWD:DUHKRXVHV\REWHQHU UHSRUWHVµGHLQIRUPDFLyQ S/D WHFQRORJtD 2/$3 FRPPSOHPHQWD ODV DFWLYLGDGHV GH 'DWD 0LQLQJ \ VXSHUDODVSRVLELOLGDGHVGHO64/ Dat a Mining y OLAP S/DV KHUUDPLHQWDV GH UHSRUWLQJ 2/$3 \ FRQVXOWD UHVSRQGHQ HIHFWLYDPHQWH SDUD OD FRQVWUXFFLyQ GH PRGHORV GHVFULSWLYRV \ UHWURVSHFWLYRV SDUD FRQILUPDU R UHFKD]DU KLSyWHVLV SUHYLDV GHO XVXDULR

18 Dat a Mining y OLAP S/DV KHUUDPLHQWDV GH 'DWD 0LQLQJ SHUPLWHQ HQFRQWUDU SDWURQHV QR HYLGHQWHV HQ ORV JUDQGHV YRO~PHQHV GH LQIRUPDFLyQ GHO ': \ SURSRQHU PRGHORVSUHGLFWLYRV Qué es la Est adíst ic a S(V OD GLVFLSOLQD TXH H[WUDH LQIRUPDFLyQ JHQHUDO D SDUWLU GH GDWRVHVSHFtILFRV S(VHOHVWXGLRGHODHVWDELOLGDGHQOD YDULDFLyQ S(V HO DUWH GH H[DPLQDU VXPDUL]DU \ H[WUDHU FRQFOXVLRQHV D SDUWLU GH ORVGDWRV

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20 Dat a Mining e IA S/D,QWHOLJHQFLD$UWLILFLDO VHLQWHJUD D OD 0LQHUtD GH 'DWRV D SDUWLU GH ODVUHGHVQHXURQDOHVDUWLILFLDOHV S6H XWLOL]DQ SDUD FRQVWUXLU PRGHORV SUHGLFWLYRV QR OLQHDOHV TXH DSUHQGHQ DWUDYpVGHHQWUHQDPLHQWR\TXHVH DVLPLODQDORVPRGHORVGHUHGHVGH QHXURQDVELROyJLFDV Redes neuronales S/DVUHGHVQHXURQDOHVVRQDGHFXDGDV SDUDSUREOHPDVGHWLSRSUHGLFWLYR S8QSUREOHPDDSURSLDGRSDUDXQDUHG QHXURQDOWLHQHWUHVFDUDFWHUtVWLFDV Se compr enden clar ament e los I NPUTS Se compr ende clar ament e el OUTPUT Exist en ej emplos (exper iencia) suf icient es par a ent r enar a la r ed

21 Los m odelos neuronales S/D UHG QHXURQDO QR SURGXFH UHJODV H[SOtFLWDVTXHGHVFULEDQHOPRGHOR S8QPRGHORQHXURQDOHVWDQEXHQRFRPROR HV HO VHW GH GDWRV XVDGR SDUD HQWUHQDU ODUHG S(O PRGHOR HV HVWiWLFR \ GHEH VHU H[SOtFLWDPHQWH DFWXDOL]DGR DJUHJDQGR HMHPSORV UHFLHQWHV \ UHHQWUHQDQGR OD UHGSDUDDVHJXUDUVXYLJHQFLD\XWLOLGDG Los m odelos neuronales S&RQ PRGHORV QHXURQDOHV VH SXHGH DWDFDU XQD JUDQ YDULHGDG GH SUREOHPDV \ SURGXFLU EXHQRV UHVXOWDGRV D~Q HQ GRPLQLRV FRPSOHMRV FRQ YDULDEOHV FRQWLQXDV\FDWHJyULFDV S6RQ DSURSLDGRV SDUD WDUHDV GH FODVLILFDFLyQ \ SUHGLFFLyQ FXDQGR ORV UHVXOWDGRV GHO PRGHOR VRQ PiV LPSRUWDQWHV TXH FRPSUHQGHU FyPR IXQFLRQDHOPRGHOR

22 Cust om er Relat ionship Managem ent S(V HO SURFHVR TXH DGPLQLVWUD OD UHODFLyQ HQWUH OD FRPSDxtD \ VXV FOLHQWHV S3DUD TXH UHVXOWH H[LWRVR UHVXOWD QHFHVDULR LGHQWLILFDU ORV SDWURQHV GHFRQVXPR\FRPSRUWDPLHQWRGHORV FOLHQWHV Dat a Mining - CRM S'DWD 0LQLQJ VH XWLOL]D SDUD VLVWHPDWL]DU ORV SURFHVRV GH E~VTXHGD GH ORV SUHGLFWRUHV GH FRPSRUWDPLHQWR GH ORV FOLHQWHV HQ ODVHWDSDVGHGLVHxRGHFDPSDxDV S7DPELpQ VH DSOLFD SDUD OD PHGLFLyQ GHORVUHVXOWDGRVGHODFDPSDxD\OD UHDOLPHQWDFLyQGHO&50

23 Problem as t ípic os de Dat a Mining S&ODVLILFDFLyQ S(VWLPDFLyQ S3UHGLFFLyQ S$JUXSDPLHQWRDSDUWLUGH UHJODVGH DVRFLDFLyQ S&OXVWHULQJ S'HVFULSFLyQ\YLVXDOL]DFLyQHWF Problem a de Clust ering $JUXSDUDORVFOLHQWHVVHJ~QVXVLQGLFDGRUHV 55HFHQF\ ))UHFXHQFLD 0 0RQWR HWF HQVHJPHQWRVGHFRPSRUWDPLHQWRKRPRJpQHR 5HVXOWDGR &OLHQWHV +HDY\ 0HGLXP /LJKW HWF (OGHODIDFWXUDFLyQVHFRQFHQWUDHQHO FOXVWHU+HDY\GHORVFOLHQWHV /RV FOLHQWHV +HDY\ VRQ FDVDGRV FRQ KLMRV WUDEDMDGRUHV DXWyQRPRV FRQ XQ LQJUHVR VXSHULRUD

24 Problem a de Clasific ac ión &ODVLILFDU XQ QXHYR FOLHQWH GH DFXHUGR D VX SHUILO VRFLRGHPRJUiILFR FRPR SRWHQFLDO FOLHQWH+HDY\0HGLXP/LJKW Problem a de Est im ac ión (VWLPDU HO FRQVXPR GH XQ GHWHUPLQDGR UXEUR GH DUWtFXORV GH XQ JUXSR FOLHQWHV HQ HO SUy[LPR WULPHVWUH (VWLPDU HO /79 /LIH 7LPH 9DOXH SRWHQFLDOGHXQQXHYRFOLHQWH

25 Problem a de Predic c ión 3UHGHFLUHODEDQGRQRGHXQFOLHQWH FKXUQLQJDWULWWLRQ 3DUDXQDFRPSDxtDGHWHOHIRQtD FHOXODU 3DUDXQD$)-3 3DUDXQDWDUMHWDGHFUpGLWR Problem a de Asoc iac ión (QFRQWUDUODVUHJODVTXHGHWHUPLQDQ HOFURVVWUDIILFHQWUHSURGXFWRV SDUDORVFOLHQWHVGHXQ%DQFR3RU HMHPSOR &XDQGRXQFOLHQWHVHDFWLYDHQ&DMD GH$KRUURVHOVLJXLHQWHSURGXFWR HQGRQGHVHDFWLYDHV3UpVWDPRV SHUVRQDOHV(VWHSDWUyQRFXUUHHQ HOGHORVFDVRVµ

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27 Problem as usuales S3URJUDPDVGHPLOODMH\ILGHOL]DFLyQ S&RQVROLGDFLyQGH%DVHVGH'DWRV SURSLDVFRQIXHQWHVH[WHUQDV S:HEPLQLQJ\DQiOLVLVGHWUiILFR\ XVRGHUHFXUVRVGHHEXVLQHVV S'HILQLFLyQ GH PDUFRV PXHVWUDOHV SDUD LQYHVWLJDFLRQHV GH PHUFDGR \ HQFXHVWDVGHFXVWRPHUVDWLVIDFWLRQ La elec c ión del m odelo para Dat a Mining 3ULQFLSDOHVREMHWLYRVGHOSURFHVRGH'DWD 0LQLQJ pr edicción descr ipción (O PpWRGR D XWLOL]DU GHSHQGH GH ORV REMHWLYRVSHUVHJXLGRVSRUHODQiOLVLVSHUR WDPELpQ GH OD FDOLGDG \ FDQWLGDG GH ORV GDWRVGLVSRQLEOHV

28 Fuente: Mining your Own Business Data Using DB2 Intelligent Miner for Data Cóm o selec c ionar una pot enc ial aplic ac ión de DM &RQVLGHUDFLRQHVSUiFWLFDV 3RWHQFLDOLPSDFWRVLJQLILFDWLYR5HODFLyQ FRVWREHQHILFLR 1RKD\RWUDDOWHUQDWLYD ([LVWHVRSRUWHLQVWLWXFLRQDO 1RH[LVWHQLPSHGLPHQWRVOHJDOHVGHXVR GHODLQIRUPDFLyQ

29 Cóm o selec c ionar una pot enc ial aplic ac ión de DM Consider aciones t écnicas: 'LVSRQLELOLGDGVXILFLHQWHGHGDWRV 5HOHYDQFLDGHDWULEXWRV %DMRVQLYHOHVGHUXLGRHQORVGDWRV 3UHFLVDUHOQLYHOGHFRQILDQ]DSDUDORV UHVXOWDGRV &RQRFLPLHQWRDQWHULRUH[LVWHQWH La evaluac ión de los m odelos &XiQDMXVWDGRHVHOPRGHOR" (VFRUUHFWDVXGHVFULSFLyQGHORV GDWRVREVHUYDGRV" &XDQWDFRQILDQ]DVHSXHGHWHQHUHQ VXVSUHGLFFLRQHV" &XiQFRPSUHQVLEOHHVHOPRGHOR"

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32 Web Mining S(V HO GHVFXEULPLHQWR GH SDWURQHV VLJQLILFDWLYRVDSDUWLUGHODQiOLVLVGH OD HVWUXFWXUD FRQWHQLGRV\ XVR GH OD:HE Web Mining Tax onom y :HE0LQLQJ :HEFRQWHQW :HE6WUXFWXUH :HEXVDJH

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34 Tex t Mining S6RQQXHYDVKHUUDPLHQWDVGHVWLQDGDV D H[WUDHU LQIRUPDFLyQ GH GRFXPHQWRV QR HVWUXFWXUDGRVµ RUJDQL]DUORV VHJPHQWDUORV LQGH[DUORV Problem as de Tex t Mining S'LUHFFLRQDPLHQWR DXWRPiWLFR GH HPDLOVVHJ~QVXFRQWHQLGR S&ODVLILFDFLyQ DXWRPiWLFD GH GRFXPHQWRVGHXQDLQWUDQHW S%~VTXHGD GH LQIRUPDFLyQ HQ GRFXPHQWRV GH GLVWLQWRV LGLRPDV VLPXOWiQHDPHQWH

35 Problem as de Tex t Mining S$QiOLVLV GH FRQWHQLGRV GH SiJLQDV :HE S2UJDQL]DFLyQ GH VHUYLFLRV GH E~VTXHGDHQOD:HE S([WUDFFLyQGHFRQFHSWRVGHVtQWHVLV HQ GRFXPHQWRV UHIHULGRV DO PLVPR DVXQWR Conc lusiones

36 Para qué Minería de Dat os S/D 0LQHUtD GH 'DWRV HV XQD KHUUDPLHQWDHILFD]SDUDGDUUHVSXHVWD SUHJXQWDVFRPSOHMDVGH,QWHOLJHQFLDGH 1HJRFLRV S/DV KHUUDPLHQWDV GLVSRQLEOHV SHUPLWHQ DXWRPDWL]DU SDUWH GH OD WDUHD GH HQFRQWUDU ORV SDWURQHV GH FRPSRUWDPLHQWRRFXOWRVHQORVGDWRV S3HUR«Qué no puede aut om at izarse (t odavía) S/D HOHFFLyQ GH ORV SUREOHPDV GH QHJRFLR FDQGLGDWRVSDUDWDUHDVGH'DWD0LQLQJ S/D LGHQWLILFDFLyQ \ UHFROHFFLyQ GH ORV GDWRV TXH FRQWLHQHQ OD LQIRUPDFLyQ EXVFDGD S(O PDVDMHR \ WUDWDPLHQWR GH ORV GDWRV TXHSRVLELOLWDODE~VTXHGDGHSDWURQHV S(OGLVHxR\FiOFXORGHYDULDEOHVGHULYDGDV

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44 E s ta d is tic a s Clu s te r ,0 0 % d e p o b la c ió n 'HVFULSWLYRVJHQHUDOHV S o lte Dro ivo rc ia d o /Viud o Ca s a d o s c io s e d a d e s ta d o _civil N o tra b acja ue nta P ro p ia R e la c io n d e p e n d e nc ia Ma s c ulino F e m e nin o S i N o o c up s e xo hijo s a vg tc kt fre c u p e s o s Crit erios de segm ent ac ión S6H WRPDQ FRPR YDULDEOHV DFWLYDVµ ODV TXH FRUUHVSRQGHQ DO FRPSRUWDPLHQWRGHFRQVXPR S6H WRPDQ FRPR YDULDEOHV VXSOHPHQWDULDV ORV DWULEXWRV VRFLRGHPRJUiILFRV

45 Credit Card 1 Masculino Femenino Divo So ltero rciado /Viud o Casado No Cuenta trabajapropia Si Relacio n d ep end encia No scios [se xo] [estad o_ civil] [ocup] [hijos ] fre cu pesos avgtckt [edad] 55 2 Divo So ltero rciado /Viud o Casado No Cuenta trabajapropia Masculino Femenino Relacio n d epend encia Si No s cios [estad o_ civil] [ocup] [se xo] pe s os [hijos ] fre cu [e da d] a vgtckt 27 0 Divo So ltero rciado /Viud o Casado No Cuenta trabajapropia Si Relacio n d ep end encia No Masculino Femenino 18 scios fre cu pesos [estad o_ civil] [ocup] [hijos ] [se xo] a vgtckt [e da d] Credit Ca rd Clus ter 2 Tienen 4 o más débitos automáticos Casados S o ltedivorcia ro do /Viudo Ca s a d o 27,21% de pobla ción Trabajo Cta Propia No tra b acue ja nta P ro p ia R e la cio n d e p e nd e nc ia s cios [e s tado_civil] [ocup] Ma s c ulino Fe me nino Saldo >>> S i No Varones Con hijos [s e xo] Uso frecuente Edad pe s os [hijos ] Ticket >>> fre cu [e dad] a vgtckt

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47 Algorit m os S&+$,'&KL6TXDUHG$XWRPDWLF 'HWHFWLRQ S& 57 &ODVVLILFDWLRQ DQG 5HJUHVVLRQ7UHH S&4XHVW\RWURV S,QWHOOLJHQW 0LQHU XWLOL]D XQD YDULDQWHGH& 57 Arbol de c om port am ient o Si tiene 4 o más débitos automáticos y un saldo > $ 727 entonces su probabilidad de pertenecer al cluster 2 es del 99%

48 Arbol soc iodem ográfic o Mark et Bask et Analysis S(OSUREOHPD6HWUDWDGHHQFRQWUDU ODV UHJODV GH DVRFLDFLyQ TXH RUJDQL]DQ ORV SHGLGRV GH WRSSLQJVµ H[WUD GH XQD SL]]HUtD D SDUWLU GHO DQiOLVLV GH XQ FRQMXQWR GH WLFNHWVGHYHQWD

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54 Reglas ŒU 6Ž R Œ Ž UŽ šœ W 6 Hongos Pepperoni Queso Hongos --> Pepperoni Hongos --> Queso Queso --> Pepperoni Hongos + Pepperoni --> Queso Hongos + Queso --> Pepperoni Queso + Pepperoni --> Hongos Pueden descartarse por bajo soporte Reglas significativas Ot ro ejem plo de MBA S/D DVRFLDFLyQ VH SODQWHD HQWUH ORV WRSSLQJV GH ODV SL]]DV \ ODV EHELGDV S/RV JUiILFRV GH UHJODV SHUPLWHQ YLVXDOPHQWH LGHQWLILFDU UHJODV FRQ EXHQVRSRUWHFRQILDQ]D\OLIW

55 Reglas Soporte (%)Confianza(%) Tipo Elevación Cuerpo de regla Cabecera de regla [Hongos]+[Otra bebida] ==> [Pepperoni] [Cerveza]+[Pepperoni] ==> [Hongos] [Cerveza]+[Queso] ==> [Hongos] [Hongos]+[Pepperoni] ==> [Cerveza] [Cerveza] ==> [Hongos] [Hongos] ==> [Cerveza] [Hongos]+[Queso] ==> [Cerveza] [Pepperoni]+[Queso] ==> [Gaseosa] [Hongos]+[Pepperoni]+[Queso] ==> [Cerveza] [Hongos]+[Gaseosa] ==> [Queso] [Gaseosa]+[Pepperoni] ==> [Queso]

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