Model FSM w zastosowaniu do klasyfikacji.

Transkrypt

1 Model FSM w zastosowaniu do klasyfikacji. 5DIDá$GDPF]DN:áRG]LVáDZ'XFK.DWHGUD0HWRG.RPSXWHURZ\FK8QLZHUV\WHW0LNRáDMD.RSHUQLND XO*UXG]LG]ND7RUXHPDLO^UDDGGXFK`#SK\VXQLWRUXQSO Streszczenie 6LHFL )60 PDM SURVW VWUXNWXU SRGREQ GR VLHFL 5%) MHGQDN G]LNL X*\FLX VHSDUo- ZDOQ\FK IXQNFML WUDQVIHUX ]DPLDVW UDGLDOQ\FK PDM V]HUV]H ]DVWRVRZDQLH 2PyZLRQR Dr- FKLWHNWXU LQLFMDOL]DFM NRQVWUXNW\ZLVW\F]Q\ DOJRU\WP XF]HQLD RSW\PDOL]DFM VLHFL Rbroty zlokalizowanych funkcji transferu, rozpoznawanie wektorów w czasie klasyfikacji RUD] PR*OLZRFL ]DVWoVRZD GR HNVWUDNFML UHJXá 1. Wprowadzenie :G*HQLXGR]UR]XPLHQLDOXG]NLHMLQWHOLJHQFMLLXP\VáXZ\Uy*QLüPR*QDGZDSDUDG\JPDW\ 3LHUZV]\] QLFK V]WXF]QD LQWHOLJHQFMD ED]XMH QD SU]HWZDU]DQLX V\PEROLF]Q\P D ZLF (Uó- GáHP V WX SURFHV\ SR]QDZF]H Z\VRNLHJR SR]LRPX GUXJL VLHFL QHXURQRZH Z\ZRG]VL] QHXURG\QDPLNLLLQVSLURZDQHVSU]H]VWUXNWXUQHXURQRZPy]JX6LHFLQHXURQRZHSRSU]H] VZRMRGPLHQQRüZSRGHMFLXGRSUREOHPXLQWHOLJHQFMLLXP\VáXZQRV]QRZHPR*OLZRFL GRG]LHG]LQ\V]WXF]QHMLQWHOLJHQFML'RW\FKF]DVVLHFLQHXURQRZHZ\GDMVLE\üQDMOHSV]\P UR]ZL]DQLHPGOD]DGDSR]QDZF]\FKQLVNLHJRSR]LRPXWDNLFKMDNSUREOHP\ZLG]HQLDF]\ UR]SR]QDZDQLDPRZ\OXEWH*GODSURVW\FK]DGDNODV\ILNDF\MQ\FKSU]H]FRVRQHZSHZLHQ VSRVyE RJUDQLF]RQH Z LFK PR*OLZRFLDFK UHDOL]DFML SUHGHILQLRZDQ\FK VWUXNWXU ZLHG]\ L Z X*\FLXW\FKVWUXNWXUZVHNZHQF\MQ\PSURFHVLHSU]\F]\QRZ\P1LHPDZWSOLZRFL*HZ\*- V]H IXQNFMH SR]QDZF]H V UH]XOWDWHP DNW\ZQRFL Py]JX D ZLF SRZLQQR E\ü PR*OLZH LFK odtworzenie przez sieci neuronowe [2], [4], [15]-DVQ\PMHVW*HREHFQ\UR]ZyMVLHFLQHXUo- QRZ\FKMHVWSRZL]DQ\]EUDNLHPPRGXODUQRFLLUDF]HMQLHZLHON]áR*RQRFLPRGHOXQL*] LFK ZHZQWU]Q\P RJUDQLF]HQLHP MDNR PRGHOX 'X*R MX* ZLDGRPR R V]F]HJyáDFK SURFHVyZ QHXURQRZ\FKRGSRZLHG]LDOQ\FK]DG]LDáDQLHPy]JXLQHXURG\QDPLN2EHFQLHQDZHWQLHNWó- UHG]LDá\SVyFKRORJLLNRU]\VWDM]RVLJQLüneurodynamiki [16]. &]\MHVWPR*OLZH]UR]XPLHQLHSURFHVyZP\ORZ\FKEH]SRUHGQLR]SURFHVyZQHXURQRZ\FK ZPy]JX":\GDMH VL*H QLH 1DZHW Z FKHPLL L IL]\FH NRQFHSFMH IHQRPHQRORJLF]QH NWyUH QLHVáDWZRUHGXNRZDOQHGRIXQGDPHQWDOQ\FKRGG]LDá\ZDZFL*VZX*\FLX7HRULHPDNUo- VNRSRZHZ]DVDG]LHVUHGXNRZDOQHGRPLNURVNRSRZ\FKZSUDNW\FHMHGQDNEDUG]LHMRZRFQH MHVWSU]\EOL*HQLHIHQRPHQRORJLF]QHGR]áR*RQ\FKV\VWHPyZ-]\NLQHXURORJLLLSV\FKRORJLL V]XSHáQLHUy*QH:\GDMHVLMHGQDN*HPXVL LVWQLHü WHRULD SR]ZDODMFD X]\VNDü NRQFHSFMH SV\FKRORJLF]QHMDNRDSURNV\PDFMHQHXURG\QDPLF]QHJRSRGHMFLDGRG]LDáDQLDPy]JX*áyw- Q\PLFHODPLWDNLHMWHRULLV

2 1. :SURZDG]HQLH DSURNV\PDFML GR QHXURG\QDPLNL SU]\ VSHáQLHQLX IDNWyZ QHXURELRORJLFz- Q\FK SURZDG]FHM GR QRZHM PDWHPDW\F]QHM NRQFHSFML EH]SRUHGQLR RSLVXMFHM VWDQ\ poznawcze. 2. 8*\FLHW\FKNRQFHSFMLMDNRM]\NDGR]EXGRZDQLDWHRULLV\VWHPXSR]QDZF]HJR 3. =DVWRVRZDQLHWHMWHRULLGRZ\MDQLHQLD FHFK SURFHVX SR]QDZF]HJR F]áRZLHND WDNLFK MDN LGHQW\ILNDFMDDVRFMDFMDJHQHUDOL]DFMDUy*QHVWDQ\XP\VáX 4..RQVWUXNFMD V\VWHPX DGDSWDF\MQHJR RGSRZLDGDMFHJR VSHF\ILNDFMRP V\VWHPX NWyU\ E- G]LHXF]\áVL] SU]\NáDGyZ L RJyOQ\FK SUDZ ZQLRVNRZDá X*\ZDá QDWXUDOQHJR M]\ND L NWyU\EG]LHVSHáQLDáLQQHIXQNFMHSR]QDZF]H =JRGQLH]GXFKHP$OODQD1HZHOOD8QLILHGWKHRULHVRIFRJQLWLRQWHRULDSRZLQQDE\üZVSo- PDJDQD SU]H] RSURJUDPRZDQLH SR]ZDODMFH ]ZHU\ILNRZDü SU]HVáDQNL L PRGHOH SU]H] QL XWZRU]RQH6\VWHP62$5VWZRU]RQ\SU]H]1HZHOODLMHJRZVSyáSUDFRZQLNyZED]XMHQDWZo- U]HQLXUHJXáDOHQLHPDQLFZVSyOQHJR]QHXURELRORJL0R*HE\üX*\WHF]Q\ZPRGHORZDQLX SHZQ\FKIXQNFMLSR]QDZF]\FKDOHQLHSRPR*HQDP]UR]XPLHüSRZL]DQLDW\FKSURFHVyZ] G\QDPLN]DFKRG]FZPy]JX6\VWHP)60[1]MHVWLQVSLURZDQ\QDG]LDáDQLXPy]JXLGo- VWDUF]DPR*OLZRFLQLHW\ONRPRGHORZDQLDDOHUyZQLH*UR]XPLHQLDSURFHVyZSR]QDZF]\FKL LFKUHODFML]G\QDPLNPy]JX 0RGHOHIXQNFMLPy]JXZ\PDJDMV]HUHJXDSURNV\PDFML:SLHUZV]\PNURNXZSURZDG]DVL PRGHO QHXURQX MDNR XU]G]HQLD HOHNWU\F]QHJR [15] SU]H] FR GRNRQXMH VL GUDVW\F]QHJR uproszczenia z punktu widzenia procesów biochemicznych i bioelektrycznych. Ta aproksy- PDFMD SR]ZDOD X*\ü Z PRGHOX W\ONR NLONX SDUDPHWUyZ WDNLFK MDN SUyJ Z]EXG]HQLD L ZDJL V\QDSW\F]QH -HVW UyZQLH* NRQLHF]QD GR ]UR]XPLHQLD SURFHVyZ SR]QDZF]\FK Z\*V]HJR So- ]LRPX3URFHV\SR]QDZF]HQLVNLHJRSR]LRPXUHDOL]RZDQHQDMF]FLHM SU]H] Uy*QH PDS\ Wo- SRJUDILF]QH GHILQLXM FHFK\ ZHZQWU]QHM UHSUH]HQWDFML 7H FHFK\ UHSUH]HQWXM ZLHOH W\SyZ GDQ\FK DQDORJRZH V\JQDá\ VHQVRURZH ]PLHQQH OLQJZLVW\F]QH OLF]E\ REUD]\ 3UDZG]LZH RELHNW\XP\VáXVNáDGDMVLJáyZQLH]SU]HWZRU]RQ\FKZVWSQLHGDQ\FKVHQVRURZ\FKUHSUe- ]HQWDFML REUD]NRZHM G]LDáDQLD SHUFHSF\MQHJR 2ELHNW\ XP\VáX ]QDMGXMVLZSU]HVWU]HQL XP\VáXNWyUDMHVWGODQLFK]ELRUQLNLHP1DWXUDOQSUDNW\F]QUHDOL]DFMWHMLGHLMHVWPRGXODr- QDVLHüQHXURQRZD]Z]áDPLVSHFMDOL]XMF\PLVLZRSLVLHJUXSRELHNWyZZSU]HVWU]HQLXPy- VáX:]á\WDNLHMVLHFLQLHUHSUH]HQWXMSRMHG\QF]\FKQHXURQyZDOHUDF]HMXUHGQLRQDNW\w- QRü]ELRUXNRPyUHNQHXURQRZ\FK7HJRW\SXVLHüPR*HE\üWUDNWRZDQDMDNRVLHüQHXURQRZD ED]XMFDQD]ORNDOL]RZDQ\PSU]HWZDU]DQLXOXEWH*MDNRUR]P\W\V\VWHPHNVSHUWRZ\NWyUHJR wiedza zapisana jest w postaci zbiorów rozmytych. 2. FSM 0RGHO)60)HDWXUH6SDFH0DSSLQJRSDUW\MHVWQDHVW\PDFMLJVWRFLUR]NáDGXSUDZGRSo- GRELHVWZDSUH]HQWRZDQ\FKGDQ\FK3DWU]F]Uy*Q\FKSHUVSHNW\ZPR*QDJRXZD*Dü]DVLHü QHXURQRZSRGREQGRVLHFL]UDGLDOQ\PLIXQNFMDPLED]RZ\PLFKRFLD*IXQNFMHQLHPXV]D E\üUDGLDOQHW\ONRVHSDURZDOQHV\VWHPQHXURUR]P\W\DNW\ZQRüZ]áyZVLHFL]VHSDURZDl- Q\PL IXQNFMDPL WUDQVIHUX PR*QD SU]HDQDOL]RZDü X*\ZDMF NRQFHSFML ]ELRUyZ UR]P\W\FK URG]DMV\VWHPXRSDUWHJRQDODGDFKSDPLFLPHPRU\EDVHGV\VWHPV\VWHPVDPRRUJDQL]XM- F\VLDQDZHWMGURV\VWHPXHNVSHUFNLHJRZ\NRU]\VWXMFHJRZLHG]UR]P\WOXERIHUXMFHJR SU]\GDWQHKHXU\VW\NLZSURFHVLHV]XNDQLDUR]ZL]D6NáDGRZHZHNWRUDZHMFLRZHJRLZ\j- FLRZHJRGHILQLXMUD]HPSU]HVWU]HFHFK1DSRGVWDZLHGDQ\FKWUHQLQJRZ\FKVWDQRZLF\FK SURWRW\S\ZSU]HVWU]HQLFHFKWZRU]\VLUR]P\WHRELHNW\UHSUH]HQWXMFHáF]Q\UR]NáDGSUDw- GRSRGRELHVWZDGODZHNWRUyZZHMFLRZ\FKLZ\MFLRZ\FK5R]NáDGWHQPR*HE\üX*\W\GR DSURNV\PDFMLQLH]QDQ\FK]DOH*QRFLOXEGRNODV\ILNDFML

3 Zastosowanie funkcji separowalnych pozwala na przeszukiwanie przestrzeni cech pomimo Z\VWSRZDQLDZDUWRFL EUDNXMF\FK 8PR*OLZLD WR Z\V]XNDQLH Z]áD QDMEDUG]LHM RGSRZLa- GDMFHJRDNWXDOQ\PGDQ\PZHMFLRZ\PMDNUyZQLH*GRSHáQLHQLHEUDNXMFHMZDUWRFLSRSU]H] X]XSHáQLHQLHIDNWXQDSRGVWDZLHWHRULLRSLV\ZDQHMSU]H]Z\V]XNDQ\Z]Há:LHG]D]DSLVDQD ZSU]HVWU]HQLFHFKMHVWZLFX*\ZDQDZSURFHVLHSU]HV]XNLZDQLDZWDNLVDPVSRVyEMDNZLe- G]DKHXU\VW\F]QDX*\ZDQDMHVWSU]H]HNVSHUWDGR]PQLHMV]HQLDSU]HVWU]HQLSRV]XNiZD 0RGHO)60PR*HE\üUyZQLH*]DVWRVRZDQ\GRRGNU\ZDQLDZLHG]\SUDZNWyUHPRJ]RVWDü Z\GHGXNRZDQH]SU]\NáDGyZ3UDZDWHPRJE\üUHSUH]HQWRZDQHSU]H]IXQNFMHJDXVVRZVNLH ZyZF]DVUR]P\FLHIXQNFMLJDXVVRZVNLHMRGSRZLDGDMFHMGDQHPXIDNWRZLMHVWPLDU]DXIDQLD GRWHJRIDNWXJG]LH]DXIDQLHED]XMHQDOLF]ELH]DSUH]HQWRZDQ\FKSU]\NáDGyZ 7RSRJUDILF]QDVWUXNWXUDSU]HVWU]HQLFHFKPR*HSRGOHJDüRJUDQLF]HQLRP]ZL]DQ\P]V\PEo- OLF]QZLHG]DSULRU\F]Q]DOH*QRFLSRPLG]\HOHPHQWDPLZHNWRUDZHMFLRZHJR6]NLHOHW WHMVWUXNWXU\WZRU]\VLNRU]\VWDMF]PHWRGLQLFMDOL]DFMLRSDUW\FKQDNODVWHU\]DFMLDV]F]HJyá\ XVWDODMVLZZ\QLNXSURFHVXXF]HQLD :SHZQ\PVHQVLH MHVW WR ZLF PHWDPRGHO JG\* PR*OLZDMHVWUy*QDVSHF\ILNDFMDMHJRPDWHPDW\F]Q\FKDVSHNWyZ3LHUZRWQLQVSLUDFMGRMHJR VWZRU]HQLD E\áD SUyED ZSURZDG]HQLD SRUHGQLHJR SR]LRPX RSLVX IXQNFML SR]QDZF]\FK MDNR SU]\EOL*HQLDGRneurodynamiki [2]Z\VRNDDNW\ZQRüQHXURQyZZ\V\áDMF\FKLPSXOV\RSi- V\ZDQD MHVW SU]H] GX* JVWRü SUDZGRSRGRELHVWZD Z W\P REV]DU]H SU]HVWU]HQL NWyU\ Rd- SRZLDGD NRPELQDFML FHFK NRQLHF]Q\FK GR Z\ZRáDQLD WDNLHM DNW\ZQRFL 3UREDELOLVW\F]Q\ punkt widzenia jest bardzo przydatny do opisu sieci neuronowych [3]. : WHM SUDF\ RJUDQLF]\P\ VL W\ONR GR]DVWRVRZDQLD PRGHOX)60 GR]DJDGQLH NODV\ILNDFML SRGQDG]RUHP3U]H]SRMFLHNODV\ILNDFMLUR]XPLHVLG]LHOHQLHGRZROQHJR]ELRUXHOHPHQWyZ QDJUXS\GRNWyU\FK]DOLF]DVLHOHPHQW\Uy*QLFHVLDOHSRGREQHWMPDMFHZáDVQRFLZy- Uy*QLDMFH GDQ JUXS =ELyU HOHPHQWyZ QDOH*F\FK GR MHGQHM JUXS\ QD]\ZDQ\ MHVW NODV D ND*G\HOHPHQWNODV\±RELHNWHP:NODV\ILNDFMLSRGQDG]RUHPVWUXNWXUDNDWHJRULLMHVW]QDQD F]\OLG\VSRQXMHVLFKDUDNWHU\VW\NNODV]NWyU\FKSRFKRG]RELHNW\.ODV\ILNDWRU\RSDUWHQD sieciach neuronowych na podstawie zadanego zbioru N SU]\SDGNyZ]ZDQHJRFLJLHPWUHQLngowym (X i, C i ), i= 1..N, gdzie X jest m-z\pldurz\p ZHNWRUHP FHFK RSLVXMF\P GDQ\ obiekt, natomiast C i MHVWRGSRZLHGQLR]DNRGRZDQHW\NLHWNODV\GRSDVRZXMSDUDPHWU\Ddaptacyjne W (SURFHVWHQQD]\ZDVLXPRZQLHÄXF]HQLHP ZWDNLVSRVyEE\GRNRQDüSRQL*- V]HJRSU]\EOL*RQHJRPDSRZania f( Xi; W) = Ci gdzie fmhvwixqnfmnwyuuhdol]xmhvlhü-hvwwrrgz]rurzdqlhsu]\eol*rqhjg\*qlhz\pa- JDP\]Z\NOHE\VLHüGDZDáDQDZ\MFLXGRNáDGQLHZDUWRüC i DMHG\QLHZDUWRüSR]ZDODMFD Z\UD(QLHRGUy*QLüC i od C j,orüsdudphwuyzdgdswdf\mq\fkmdnldojru\wpxf]hqld]doh*rg architektury sieci. 3. Architektura sieci FSM. 3RZD*Q\P SUREOHPHP ZLHOX DOJRU\WPyZ UHDOL]XMF\FK PRGHOH VLHFL QHXURQRZ\FK MHVW WDNL GREyUDUFKLWHNWXU\VLHFLOLF]E\XNU\W\FKQHXURQyZOLF]E\ZDUVWZXNU\W\FKWRSRORJLLSRá- F]HDE\X]\VNDüMDNQDMOHSV]JHQHUDOL]DFM,VWQLHMHZLHOHWHFKQLNRSW\PDOL]DFMLDUFKLWHNWu- U\SURZDG]F\FKGRWHJRFHOX2EV]HUQDNODVDPHWRGRSDUWDMHVWQDDOJRU\WPDFKNRQVWUXNWy- ZLVW\F]Q\FK SUyEXMF\FK ZEXGRZDü RSW\PDOL]DFM DUFKLWHNWXU\ VLHFL Z DOJRU\WP XF]HQLD 6WRVXMHVLWU]\WHFKQLNLNRQVWUuowania sieci:

4 1. 5R]SRF]\QD VL]VLHFL SRVLDGDMFGX* QDGPLDURZ OLF]EZ]áyZ NWyUH Z PLDU PR*OLZRFLVXVXZDQHSRGF]DVXF]HQLD 2. 7ZRU]\ VL VLHü RG ]HUD W]Q QD SRF]WNX LVWQLHMH W\ONR ZDUVWZD ZHMFLRZD L Z\MFLRZD QDWRPLDVWZDUVWZ\XNU\WHMQLHPDZFDOHOXEWH*MHVWDOH]QLHZLHONOLF]EZ]áyZ: WUDNFLH XF]HQLD VWRSQLRZR GRVWDZLDQH V NROHMQH QHXURQ\ RUD] HZHQWXDOQLH NROHMQH ZDr- VWZ\XNU\WH'RWHMNDWHJRULL]DOLF]\üPR*QDWDNLHPRGHOHVLHFLMDNNRUHODFMDNDVNDGRZD VLHü5$1MDNLZHUVMPRGHOX)60MHOLQLHVWRVXMHP\ZVWSQHMLQLFMDOL]DFML 3. 6LHü GRSDVRZXMH VZRM VWUXNWXU GR QDSá\ZDMF\FK GDQ\FK ]PLHQLDMF ]ár*rqrü SU]H] GRGDZDQLHXVXZDQLHLáF]HQLHQHXURQyZ6LHü)60QDOH*\GRWHMNDWHJorii. :VLHFL)60Z\VWSXMW\ONRWU]\ZDUVWZ\QHXURQyZZHMFLRZDXNU\WDLZ\MFLRZD/LF]ED Z]áyZZZDUVWZLHZHMFLRZHMMHVWXVWDORQDQDSRF]WNXSURFHVXXF]HQLDLMHVWUyZQDZ\PLa- URZLZHNWRUyZZHMFLRZ\FK:ZDUVWZLHZ\MFLRZHMZ\VWDUF]\W\ONRMHGHQZ]HáPR*QDWH* X*\ZDüMHGQHJRZ]áDQDMHGQNODVNWyUHJR]DGDQLHPMHVWRNUHOHQLHQDSRGVWDZLHZ]Eu- G]HQHXURQyZZZDUVWZLHXNU\WHMGRNWyUHMNODV\QDOH*\ZHNWRUZHMFLRZ\X:]á\ZDr- VWZ\XNU\WHMSRáF]RQHV]HZV]\VWNLPLQHXURQDPLZDUVWZ\ZHMFLRZHMRUD]]Z]áHPZ\j- FLRZ\P6LHü)60PR*HPLHüVWUXNWXUPRGXáRZVNáDGDMFVL]NLONXSRGVLHFLVSHFMDOi- ]XMF\FK VL Z NODV\ILNDFML GDQ\FK ZHMFLRZ\FK RNUHORQ\FK SU]H] FHFK\ MHGQHJR W\SX [4], ale dla celów tutaj przedstawionych nie jest ona wykorzystywana. x 1 x 2 s(x) 1 s 2 W 1 W 2 Informacje dodatkowe :VSyáF]\QQLN zaufania Σ FSM(x) x 3 x 4 s s 3 4 W 3 W 4 W 5 s 5 Architektura sieci FSM :V]\VWNLHZ]á\ZZDUVWZLHXNU\WHMUHDOL]XMGRZROQIXQNFMIDNWRU\]RZDOQ *;'σ. :DUXQHNIDNWRU\]RZDOQRFLSR]ZDODWUDNWRZDüND*G\]Z\PLDUyZMDNRQLH]DOH*Q\RGSR]o- VWDá\FK)DNWRU\]RZDOQHIXQNFMHWUDQVIHUXPDMDSRVWDü = G( XR ;, σ) G ( X ; R, σ ) i i i i i JG]LH ND*G\ ]H VNáDGQLNyZ VSDUDPHWU\]RZDQ\ MHVW SU]H] SRáR*HQLH L GRGDWNRZ\ SDUDPHWU NWyU\ GOD IXQNFML]ORNDOL]RZDQ\FK SHáQL URO G\VSHUVML&HFK FKDUDNWHU\VW\F]Q IXQNFML]Oo- NDOL]RZDQ\FKMHVWWR*HZDUWRüPDNV\PDOQRVLJDMRQHZVZRLPFHQWUXPZPLDURGGa- ODQLDVLRGFHQWUXPZDUWRüWDPDOHMHGR]HUD1DMEDUG]LHM]QDQ\PSU]\NáDGHPWHJRURG]DMX IXQNFML MHVW IXQNFMD JDXVVRZVND&KRFLD* WHRUHW\F]QLH QLH PD LQQ\FK RJUDQLF]H QD IXQNFMH

5 DNW\ZDFMLZ)60ZSUDNW\FHMHGQDNQDUD]LHVWRVRZDQHE\á\W\ONRIXQNFMH]ORNDOL]RZDQHR ODQLDVLRGFHQWUXPPR*HE\üUyZQLH*VNRNRZDFRPDPLHMVFHZSU]\SDGNXX*\FLDIXQNFML SURVWRNWQHM'RW\FKF]DVZ)60VWRVRZDQHE\á\QDVWSXMFHIXQNFMHDNW\ZDFMLJDXVVRZVNLH trapezoidalne, bicentralne [5]SURVWRNWQHLWUyjNWQH 1DMOHSV]HUH]XOWDW\]DUyZQRSRGZ]JOGHPOLF]E\SRZVWDá\FKZ]áyZMDNLJHQHUDOL]DFMLX]y- VNLZDQHE\á\GODIXQNFMLJDXVVRZVNLHM:\EyUIXQNFMLDNW\ZDFML]DOH*Q\MHVWRGFHOXNWyU\ FKFHP\X]\VNDüQSGRVWZRU]HQLDNODV\ILNDWRUDNWyUHJRG]LDáDQLHPR*HP\ZSURVW\VSRVyE SU]HOHG]LüQDMOHSLHMQDGDMVLUHJXá\ORJLF]QHNWyUHZ)60PR*QDX]\VNDüVWRVXMFIXQNFMH SURVWRNWQH8*\ZDMFQDWRPLDVWIXQNFMLJDXVVRZVNLHMPR*QDUyZQLH* X]\VNDü UHJXá\ V WR MHGQDN UHJXá\ UR]P\WH NWyU\FK LQWHUSUHWDFMD MHVW ]QDF]QLH WUXGQLHMV]D RG NODV\F]Q\FK UHJXá ORJLF]Q\FK.D*G\Z]HáXNU\W\FKDUDNWHU\]RZDQ\MHVWSU]H]SRáR*HQLHR, i rozmycie σ, które SRWU]HEQHVGRZ\OLF]HQLDIXQNFMLDNW\ZDFML3R]DW\PZ\VWSXMMHV]F]HZLHONRFLNWyUHQLH PDMZSá\ZXQDZDUWRüZ]EXG]HQLDDOHVSRWU]HEQHZWUDNFLHXF]HQLDGRRNUHOHQLDZLHl- NRFL]PLDQSR]RVWDá\FKSDUDPHWUyZ6WRPDVDm RNUHODMFDOLF]EZHNWRUyZNODV\ILNo- ZDQ\FKSU]H]GDQ\ Z]Há L F]DV SRZVWDQLD τ n, czyli numer epoki, w którejgdq\z]há So- ZVWDá 4. Inicjalizacja 3RQLHZD*DOJRU\WPXF]HQLDZ )60MHVWDOJRU\WPHPNRQVWUXNW\ZLVW\F]Q\P WR PR*QD SU]y- VSLHV]\üSURFHVXF]HQLDSRSU]H]ZVWSQHRV]DFRZDQLHOLF]E\Z]áyZXNU\W\FKLRGSRZLHGQLH ich zainicjowanie [6]2V]DFRZDQLHWRSRZLQQRE\üUDF]HMRSW\PLVW\F]QHW]QOLF]EDZ]áyZ XWZRU]RQD SRGF]DV LQLFMDOL]DFML SRZLQQD E\ü ]DQL*RQD : SU]HFLZQ\P Z\SDGNX ZVWSQD LQLFMDOL]DFMDSURZDG]LGR]E\WQLHJRUR]GUREQLHQLDLQDZHWSRX*\FLXRSW\PDOL]DFMLQLHX]\VND VLGREU\FKUH]Xltatów. ']LNL VWRVRZDQLX IXQNFML ]ORNDOL]RZDQ\FK GR XVWDOHQLD OLF]E\ Z]áyZ XNU\W\FK MDN L LFK ]DLQLFMRZDQLDPR*QDX*\üPHWRGRSDUW\FKQDJUXSRZDQLX:Z\QLNXNODVWHU\]DFMLRWU]\Pu- MHP\]ELyUVNXSLVNSURWRW\SyZZURGNXNWyU\FKXVWDZLDQHVZ]á\VLHFL3RáR*HQLHND*Ge- JR] WDN SRZVWDá\FK QHXURQyZ REOLF]DQH MHVW MDNR UHGQLD] SRáR*H GOD ND*GHJR Z\PLDUX RVREQR ZV]\VWNLFK ZHNWRUyZ ZSDGDMF\FK GR GDQHJR VNXSLVND NODVWUD 5R]P\FLD W\FK SURWRW\SyZXVWDODQHVQDSRGVWDZLHZLHONRFLRGSRZLDGDMF\FKLPNODVWUyZ*G\NWyUH] UR]P\üPDZDUWRü]HURZV]\VWNLHZHNWRU\PDMWVDPZDUWRüMHGQHM]FHFKSU]\MPRZa- QDMHVWPLQLPDOQDZDUWRüQLH]HURZD=XZDJLQDWR*HIXQNFMDDNW\ZDFMLMHVWLORF]\QHPSR SRV]F]HJyOQ\FKZ\PLDUDFKMHOLFKRüMHGQD]HVNáDGRZ\FKPDZDUWRüWRFDáDIXQNFMDDk- W\ZDFMLMHVW]HURZD7DNXVWDORQHUR]P\FLD]RVWDMQDVWSQLHSURSRUFMRQDOQLH]ZLNV]RQHSR WRDE\VLHüZSRF]WNRZHMID]LHXF]HQLDRGUD]XNODV\ILNRZDáDEH]Z]JOGXQDSRSUDZQRü ZV]\VWNLHZHNWRU\] FLJX WUHQLQJRZHJR']LNL WHPX XQLND VL SU]\SDGNRZHJR ZVWDZLDQLD Z]áyZQDSoF]WNXXF]HQLD Jednym z algorytmów stosowanych w FSM do inicjalizacji sieci jest drzewo decyzyjne budo- ZDQHQDSRGVWDZLHKLVWRJUDPXXWZRU]RQHJRGODND*GHJRZ\PLDUXRVREQR

6 Dany wymiar dzielony jest na ksu]hg]ldáyzr;qdu\vxqnx:nd*g\psu]hg]ldoh]olf]a- QDMHVWOLF]EDZHNWRUyZNWyUDGRQLHJRZSDGDR<QDU\VXQNX.D*G\]SU]HG]LDáyZPR*H E\ü áf]rq\] VVLHGQLPL SU]HG]LDáDPL WZRU]F Z WHQ VSRVyE VNXSLVNR Z SU]HVWU]HQL MHGQo- Z\PLDURZHM-H*HOLZGDQ\PZ\PLDU]HZ\VWSXMHZLHOHVNXSLVNWREGRQHRGG]LHORQHSu- VW\PL SU]HG]LDáDPL OXE WH* PLG]\ NROHMQ\PL SU]HG]LDáDPL Z\VWSL EDUG]R GX*D Uy*QLFD Z ]DZDUWRFLZHNWRUyZSU]HGVWDZLRQRWR QD SRZ\*V]\P U\VXQNX JG]LH PR*QD Z\Uy*QLü VNXSLVND=Dáy*P\*HNODVWHUUR]SRF]\QDVLRGiWHJRSU]HG]LDáXL]DMPXMHl SU]HG]LDáyZ ND*G\RV]HURNRFLs. Wówczas pozycja oraz rozmiar skupiska w oryginalnej przestrzeni mo- *H]RVWDüSU]HGVWDZLRQDZQDVWSXMF\VSRVyE C x = X min 1 σ x = ls 2 X max s = + s( i + X k min 1 ) 2 x1 = a1 b1 a1 b1 x2 x2 = a2 b2 a2 c2 a2 b2 c2 x2 x3 = a3 a3 b3 b3 V1= f(a1 ;a 2 ;a 3)g V2= f(a1 ;b 2 ;a 3)g V3= f(b1 ;a 2 ;b 3)g V4= f(b1 ;c 2 ;b 3)g a3 b3 x3 Drzewo decyzyjne.d*gh ] W\FK MHGQRZ\PLDURZ\FK VNXSLVN PR*H ]RVWDü QDVWSQLH ]U]XWRZDQH QD ZLHOH URzseparowanych N-Z\PLDURZ\FKVNXSLVN3RGF]DVLQLFMDOL]DFMLZHNWRU\DQDOL]RZDQHVZND*- G\PZ\PLDU]HQLH]DOH*QLHWDNZLFZSLHUZV]\PZ\PLDU]HGDQ\ZHNWRUPR*HQDOH*HüQSGR

7 i j l skupiska C 1, w drugim wymiarze do skupiska C 2 D*ZUHV]FLHZN-tym wymiarze CN.D*G\ taki N-Z\PLDURZ\NODVWHUPR*HE\üSU]HGVWDZLRQ\MDNRáDFXFKQL*HMZ\PLDURZ\FKVNXSLVN i j l C 1 > C2 >... > CN VWGWHJRW\SXSURFHGXUDWZRU]\GU]HZRGHF\]\MQH:OLFLDFKGU]HZD ]OLF]DQH V ZHNWRU\ NWyUH QDOH* GR GDQHJR N-wymiarowego skupiska. Gdy w przypadku NWyUHJRNROZLHN]Z\PLDUyZOLF]EDNODVWUyZMHVW]E\WGX*D]PQLHMV]RQD]RVWDMHUR]G]LHOF]Rü kfrsrzrgxmh]pqlhmv]hqlholf]e\nodvwuyzgodgdqhjrz\pldux*g\zv]\vwnlhnodvwu\v MX*XWZRU]RQHREOLF]DQDMHVWRGOHJáRüPLG]\QLPL7HVNXSLVNDPLG]\NWyU\PLRGOHJáRü jest mniejv]drg]dgdqhjrsurjxváf]rqhzmhghq : SRZ\*V]\P GU]HZLH GHF\]\MQ\P UR]G]LHOF]Rü KLVWRJUDPyZ MHVW VWRSQLRZR ]ZLNV]DQD,QQ\P UR]ZL]DQLHP RSDUW\P QD PHWRG]LH GHQGURJUDPyZ NWyUH F]DVHP SURZDG]L GR OHp- V]\FKUH]XOWDWyZMHVWVWRSQLRZH]PQLHMV]DQLHUR]G]LHOF]RFL3RF]WNRZRND*G\ZHNWRUFL- JXWUHQLQJRZHJRMHVWRGG]LHOQ\PVNXSLVNLHP:\]QDF]RQD]RVWDMHPDFLHU]RGOHJáRFLPLG]\ SRV]F]HJyOQ\PLVNXSLVNDPLLQDMHMSRGVWDZLHQDMEOL*V]HVNXSLVNDV]HVREáF]RQH&DáD SURFHGXUDWUZDWDNGáXJRD*OLF]EDVNXSLVNMHVWZ\VWDUF]DMFRPDáDOXEWH*D*RGOHJáRüPL- G]\VNXSLVNDPLMHVWZLNV]DRG]DGDQHMSURJRZHM3RQL*V]\U\VXQHNSU]HGVWDZLDVFKHPDW\Fz- QLHLGHGHQGURJUDPyZ d(c i ;c j ) c 1 c 2 c 3 c 4 c 5 c 6 c 7 c 8 Clusters Dendrogram :DGPHWRG\GHQGURJUDPyZMHVWNRQLHF]QRüWZRU]HQLDPDFLHU]\RGOHJáRFLFRZSU]\SDGNX GX*HMOLF]E\ZHNWRUyZWUHQLQJRZ\FKSURZDG]LGR]QDF]QHJRVSRZROQLHQLDSURFHVXJUXSRZa- QLD RUD] GX*HJR ]DSRWU]HERZDQLD QD SDPLü : WDNLHM V\WXDFML GREU\P UR]ZL]DQLHP MHVW zmniejszeqlhur]g]lhof]rflgdq\fk 2EOLF]HQLD ]UHJXá\ Z\NRQ\ZDQH V GOD OLF]E ]PLHQQRSU]HFLQNRZ\FK PDMF\FK EDMWRZ UHSUH]HQWDFM FR GOD GDQ\FK SU]HQRUPDOL]RZDQ\FK GR SU]HG]LDáX >@ GDMH UR]G]LHOF]Rü r = 10 7 'ODUR]G]LHOF]RFL r ZV]\VWNLHGDQH]SU]HG]LDáX [ a, a + r] PDMWVDPZDUWRü 3U]HGGRNRQDQLHPREFLFLDGRNáDGQRFL ZV]\VWNLH GDQH] FLJX WUHQLQJRZHJR SU]HVNDORZy- ZDQHVGRPDNV\PDOQHJR]DNUHVX [0,2 32 ] 32 2 X r = C( X r X min ); C = X X max min

8 1 $E\ X]\VNDü UR]G]LHOF]Rü r = PXVLP\ ]RVWDZLü k ]QDF]F\FK ELWyZ Z X k r 0R*QD WR 2 Z\NRQDüSU]H]SU]HVXQLFLHELWyZ 1 X r 33 k X ( k) = X min + Round k C 33 * 2 2 Dla k = 1wszystkie dane X V PDSRZDQH GR GZyFK NODVWUyZ GOD N RWU]\PXMHP\ GDQH RU\JLQDOQH/LF]ED]QDF]F\FKELWyZMHVW]ZLNV]DQDWDNGáXJRD*RVLJQLWD]RVWDQLHGRSXVzczalna liczba skupisk. :ID]LHJUXSRZDQLDG*\VLGRWHJRDE\SRZVWDáHNODVWU\RSLV\ZDá\MHG\QLHRGG]LHOQHZy- UD(QHVNXSLVNDGODGDQHMNODV\DQLHLFK]áR*RQVWUXNWXUZHZQWU]Q=DSHZQLDWR*HVWo- VRZDQHRV]DFRZDQLHEG]LHÄRSW\PLVW\F]QH $OJRU\WPLQLFMDOL]DFMLDXWRPDW\F]QLHZ\]QDF]D OLF]EVNXSLVNGODGDQHJRSUREOHPX3URFHVJUXSRZDQLDPR*HE\üSU]HSURZDG]RQ\GODND*GHM NODV\ RVREQR FR SR]ZDOD]QDOH(ü VNXSLVND FKDUDNWHU\VW\F]QH GOD WHM NODV\ RUD]]DLQLFMRZDü VLHüZWDNLVSRVyE DE\ ND*GD ] NODV E\áD UHSUH]HQWRZDQD SU]H] FR QDMPQLHM MHGHQ Z]Há 0R*QDWH*SURFHVJUXSRZDQLDSU]HSURZDG]LüGODZV]\VWNLFKNODVMHGQRF]HQLH:W\PSU]y- SDGNXSRGF]DVJUXSRZDQLDZ\NRU]\VWXMHVLGRGDWNRZLQIRUPDFMSU]\QDOH*QRüGRNODV\L EXGXMFVNXSLVNRDQDOL]XMHVLMHJRGRNáDGQRüW]QOLF]EZHNWRUyZ]LQWHUHVXMFHMQDVNODV\ ZVWRVXQNXGRZV]\VWNLFKZHNWRUyZQDOH*F\FKGRWHJRVNXSLVND:PRPHQFLHJG\MDNRü VNXSLVND]QDF]QLH VL SRJDUV]D SU]HU\ZD VL áf]hqlh JUXS GR WHJR VNXSLVND-HVW WR EDUG]R wygodny punkt stopu dla metody dendrogramów. 7DNZLFSURFHVXF]HQLDNWyU\QDVWSXMHSRLQLFMDOL]DFMLRGE\ZDVL]DZV]HGODVLHFLNWyUD SRVLDGDMX*MDNLHZ]á\XNU\WH 5. Algorytm Uczenia 1DZHMFLHVLHFLSRGDZDQ\MHVWZHNWRU Z\ELHUDQ\ ORVRZR] FLJX WUHQLQJRZHJR:\EyU Go- NRQ\ZDQ\MHVWZWDNLVSRVyEDE\ND*G\]ZHNWRUyZZGDQHMVHULLSRMDZLáVLGRNáDGQLH raz. *G\FDá\FLJWUHQLQJRZ\]RVWDQLH MX* SRND]DQ\ SURFHGXUD]RVWDMH SRZWyU]RQD.D*GD WDND VHULD QD]\ZDQD MHVW HSRN 3URFHV XF]HQLD WUZD WDN GáXJR D* VSHáQLRQH ]RVWDQLH NU\WHULXP zakoczenia opisane poni*ej&dá\surfhvxf]hqldsrg]lholüpr*qdqdgzlhid]\ )D]D0RG\ILNDFMDSDUDPHWUyZLVWQLHMF\FKSURWRW\SyZWMSRáR*HQHXURQyZLFKUR]P\ü mas i czasów powstania. Faza 2: Dostawianie nowych neuronów Faza I -HOLZHNWRUZHMFLRZ\ MHVW GRVWDWHF]QLH SRGREQ\ GR LVWQLHMFHJR Z]áD Z\VWDUF]\]PRG\Ii- NRZDüSDUDPHWU\RSLVXMFHWHQZ]Há3RGRELHVWZRZ\]QDF]DQHMHVWQDSRGVWDZLHRGOHJáo- FLHXNOLGHVRZHMPLG]\ZHNWRUHPZHMFLRZ\PDSRV]F]HJyOQ\PLQHXURQDPLZVLHFLOXEWH* QDSRGVWDZLHSREXG]HQLDZ]áyZ:SU]\SDGNXJG\GZD Z]á\ UHSUH]HQWXMFH Uy*QH NODV\ PDMWVDPZDUWRüIXQNFMLDNW\ZDFMLZSU]\SDGNXIXQNFMLJDXVVRZVNLFKPR*HVLWR]Ga- U]Dü U]DGNR MHGQDN Z SU]\SDGNX IXQNFML SURVWRNWQ\FK EDUG]R F]VWR Z\ELHUDQ\ MHVW WHQ NWyU\QDOH*\GRLQQHMNODV\QL*ZHNWRUZHMFLRZ\SU]H]FRZREOLF]DQLXNRFRZHMNODV\ILNa- FMLPDP\GODWDNLHJRZHNWRUDZHMFLRZHJREáG=DQDMEDUG]LHMSRGREQ\X]QDZDQ\MHVWWHQ Z]HáNWyU\MHVWQDMEOL*V]\ZVHQVLHHXNOLGHVRZ\PF]\OL min k( X R k ) ) do wektora wej- FLRZHJRX-H*HOLQDMEOL*V]\MHVWZ]Há]WHMVDPHMNODV\FRZHNWRUZHMFLRZ\GRNRQXMHP\ RSW\PDOL]DFMLMHJRSDUDPHWUyZ -H*HOL MHVW WR QHXURQ UHSUH]HQWXMF\ LQQ NODVQL*ZHNWRU

9 ZHMFLRZ\SRV]XNXMHP\Z]áDNWyU\XOHJDQDMZLNV]HPXZ]EXG]HQLX-HOLWHQZ]HáQDOH*\ GRNODV\ZHNWRUDZHMFLRZHJR WR SU]HSURZDG]DP\ MHJR RSW\PDOL]DFM Z SU]HFLZQ\P UD]LH UR]SRF]\QDVLGUXJDID]DXF]HQLDF]\OLGostawianie nowego neuronu. :REOLF]DQLXIXQNFMLDNW\ZDFMLVNDORZDQLHGDQ\FKQLHPDZSá\ZXQDZDUWRüWHMIXQNFMLSo- QLHZD*ND*G\]Z\PLDUyZUR]SDWU\ZDQ\MHVWQLH]DOH*QLH']LNLWHPXZNáDGND*GHJR]Zy- PLDUyZGRIXQNFMLDNW\ZDFML]DZV]HQDOH*\GRSU]HG]LDáX>@3RQLHZD*MHGQDNGRRNUHOenia podoelhvwzd PLG]\ Z]áHP D ZHNWRUHP ZHMFLRZ\P X*\ZDQD MHVW RGOHJáRü HXNOide- VRZDWRSU]HVNDORZDQLHGDQ\FKPR*HPLHüZSá\ZQDSURFHVXF]HQLDJG\*QRZHZ]á\PRJ E\üZVWDZLDQHZLQQ\PPLHMVFXQL*SU]HGSU]HVNDORZDQLHP'ODWHJRWH*SU]HGUR]SRF]FLHP XF]HQLDGRNRQXMHVLVWDQGDUyzacji danych. $GDSWDFMDSDUDPHWUyZSROHJDQDWDNLPLFKGRSDVRZDQLXE\]ZLNV]\üZDUWRüZ]EXG]HQLD Z]áD 'RNRQXMHP\ WHJR SRSU]H] ]PLDQ SRáR*HQLD Z]áDWDNDE\ZND*G\P Z\PLDU]H ] RVREQD]PQLHMV]\üRGOHJáRüPLG]\QLPDZHNWRUHPZHMFLRZ\P κ Ri = Ri + ( Xi Ri) m -HGQRF]HQLH ]ZLNV]DP\ UR]P\FLH Z]áD SURSRUFMRQDOQLH GR RGOHJáRFL ] ZHNWRUHP ZHj- FLRZ\PSRGREQLHMDNSRáR*HQLHGODND*GHJRZ\PLDUXRVREQRRUD]GRDNWXDOQHJRZ]Eu- G]HQLDWHJRZ]áDLRGZURWQLHSURSRUFMRQDOQLHGRF]DVXMHJR*\FLDτ τ n : (1 GXR ( ;, σ)) Xi Ri σi = σi + γ 1 + / Λ ( τ τ ) &]DV*\FLDMHVWWRUy*QLFDDNWXDOQHJRQXPHUXHSRNLτLF]DVXSRZVWDQLDZ]áDτ n (czyli nume- UXHSRNLZNWyUHMZ]HáSRZVWDá,PVWDUV]\Z]HáW\PWUXGQLHMMHVW]PLHQLDüMHJRSDUDPHWU\ DGDSWDF\MQH2F]\ZLFLHZWUDNFLHXF]HQLDQXPHUHSRNLτ XOHJDFLJáHPX]ZLNV]HQLXWDN ZLFUy*QLFDτ τ n MHVW]DZV]HGRGDWQLDOXEMHOLZ]HáSRZVWDáZDNWXDOQHMHSRFHUyZQDMHVW 0. Parametry uczenia κ, γ GRSDVRZ\ZDQH V Z VSRVyE DXWRPDW\F]Q\ LQG\ZLGXDOQLH GOD ND*- dego w]ád γ = Γ 1 + τ / ; Λ ( τ ) n n κ = Κ 1 + τ / Λ ( τ ) Parametr ΛRNUHODV]\ENRü]PQLHMV]DQLDVLSDUDPHWUyZXF]HQLDSDUDPHWUWHQXVWDORQ\MHVW QDSRF]WNXXF]HQLDLZáDFLZLHZHZV]\VWNLFKGRW\FKF]DVRZ\FK]DVWRVRZDQLDFKPLDá]Dw- V]H WDNVDP ZDUWRü QDWRPLDVW Γ i ΚV SRF]WNRZ\PL ZDUWRFLDPL SDUDPHWUyZ XF]HQLDNWyUHWU]HEDXVWDOLüSU]HGURzSRF]FLHPXF]HQLD 3RQLHZD*]PLDQD UR]P\FLD MHVW SURSRUFMRQDOQD GR G), QDWRPLDVW ZDUWRü PDNV\PDOQHJR Z]EXG]HQLDZ\QRVLWRLPZLNV]DZDUWRüZ]EXG]HQLDW\PPQLHMV]H]ZLNV]HQLHUR]Py- FLD 6WG UyZQLH* RJUDQLF]HQLH FR GR IXQNFML DNW\ZDFML DE\ MHM ZDUWRFL E\á\ ] SU]HG]LDáX >@-HOLZ]HáNODV\ILNXMHSRSUDZQLHQRZ\ZHNWRUWRMHJRPDVD]RVWDMH]ZLNV]RQDRMeden: m=m1dsrf]wnxqrzhmhsrnlpdvdzv]\vwnlfkz]áyzmhvwxvwdodqdqdzduwrü :FHOXXQLNQLFLD]E\WVLOQHJRQDNáDGDQLDVLZ]áyZUHSUH]HQWXMF\FKUy*QHNODV\QDVLHELH ZF]DVLHRSW\PDOL]DFMLSRGHMPRZDQDMHVWUyZQLH*SUyED]PQLHMV]HQLDSRGRELHVWZDGRZ]áD EGFHJR QDMZLNV]\P]DJUR*HQLHP:]Há NWyU\ E\á RSW\PDOL]RZDQ\ F]\OL Z]Há QDMEDU G]LHMSRGREQ\GRZHNWRUDZHMFLRZHJR ]RVWDMH Z\áF]RQ\ ] REOLF]H L SRV]XNLZDQ\ MHVW n

10 Z]HáQDMEDUG]LHMZ]EXG]DMF\VL-H*HOLMHVWRQ]LQQHMNODV\QL* ZHNWRU ZHMFLRZ\ QDOH*\ ]PQLHMV]\üMHJRSRGRELHVWZRSoprzez zmniejszenie przypisanego mu rozmycia: i i ( ;, ) σ = σ υ G X R σ Xi Ri 1 + / Λ ( τ τ ) :DUWRüSDUDPHWUXυ GODGX*\FKZEXG]H*!Z\QRVLGODPDá\FKZSU]\SDGNXJG\ UR]P\FLHSU]\MPXMHXMHPQZDUWRüEUDQDMHVWZDUWRüEH]Z]JOGQD &]DVDPLPR*HVL]GDU]\ü*HUR]P\FLHXOHJDJZDáWRZQHPX]PQLHMV]HQLXGODWHJRWH*ZFHOX XáDWZLHQLD SRQRZQHJR Sy(QLHMV]HJR GRSDVRZDQLD SDUDPHWUyZ RGPáDG]DP\ GDQ\ QHXURQ F]\OL]ZLNV]DP\MHJRF]DVSRZVWDQLD τ = τ + ( τ τ )/2 n n n -H*HOLMHVWRQ]WHMVDPHMNODV\WRQLHWU]HEDGRNRQ\ZDüGDOV]\FK]PLDQ-HVWWRUyZQR]QDF]QH ]H]JRG QD WR E\ Z]á\ UHSUH]HQWXMFH W VDP NODV QDNáDGDá\ VL QD VLHELH 0R*QD ZLF VWZLHUG]Lü*HSRGF]DVWHMID]\XF]HQLDQDVWSXMHVDPRRUJDQL]DFMD[6],[7] z nadzorem czyli z XZ]JOGQLeniem informacji o klasach. n 5.2. Faza II 1RZ\Z]HáZVWDZLDQ\MHVWGRVLHFLZWHG\JG\GODLVWQLHMFHJRZHNWRUDZHMFLRZHJR]DUyw- QRQDMEOL*V]\ZVHQVLHHXNOLGHVRZ\PMDNLQDMEDUG]LHMZ]EXG]DMF\VLZ]HáV]LQQHMNODV\ QL*ZHNWRUQDZHMFLXVLHFL:VSyáU]GQHSRáR*HQLDQRZHJRZ]áDVWDNLHVDPHMDNZHNWRUD ZHMFLRZHJR 1DWRPLDVW MHJR UR]P\FLH XVWDZLDQH MHVW QD SRGVWDZLH SRáR*HQLD QDMEOL*V]HJR QHXURQX7DNZLFSRdVWDZRZHSDUDPHWU\QRZRSRZVWDáHJRZ]áDPDMSRVWDü R = X m= 1 τ = τ i i n /LF]EDWZRU]RQ\FKZ]áyZZMHGQHMHSRFHMHVWograniczona i równa jest liczbie klas znajduj- F\FKVLZ]ELRU]HWHUQLQJRZ\P7DNLHRJUDQLF]HQLHXPR*OLZLDPDNV\PDOQ\UR]URVWZ]áRP LVWQLHMF\P-DNSRND]XMHGRZLDGF]HQLHEH]RJUDQLF]HQLDSRZVWDMHZLNV]DOLF]EDZ]áyZ DFR]DW\PLG]LHMDNRüJHQHUDOL]DFMLMHVWPQLHMV]DRUD]Z\GáX*DVLF]DVXF]HQLD 3RND*GHMHSRFHVSUDZG]DQDMHVWMDNRüNODV\ILNDFMLQ ND*GHJR]LVWQLHMF\FKZ]áyZRNUe- ORQD SU]H] VWRVXQHN OLF]E\ SRSUDZQLH VNODV\ILNRZDQ\FK ZHNWRUyZ GR OLF]E\ ZV]\VWNLFK ZHNWRUyZ NWyUH ÄZSDGDM Z GDQ\ Z]Há 6SUDZG]HQLH NODV\ILNDFML SROHJD QD Z\V]XNDQLX ZUyGLVWQLHMF\FKZ]áyZWDNLHJRNWyUHJRZ]EXG]HQLHMHVWQDMZLNV]HDMHGQRF]HQLHMHVW ZLNV]H RG ]DGDQHM ZDUWRFL PLQLPDOQHM SURJX -H*HOL Z]EXG]HQLD ZV]\VWNLFK Z]áyZ V SRQL*HM]DGDQHJRSURJXWRGDQ\ZHNWRUZHMFLRZ\QLHMHVWNODV\ILNRZDQ\3DUDPHWUZDUWRFL PLQLPDOQHM MHVW QD SRF]WNX XF]HQLD GX*\ SU]H] FR W\ONR ZHNWRU\ EOLVNR FHQWUXP QHXURQX EUDQHVSRGXZDJ:WUDNFLHWUZDQLDXF]HQLDSDUDPHWUWHQMHVWDXWRPatycznie zmniejszany. -H*HOLGDQ\ QHXURQ NODV\ILNXMH SRQL*HM Z\PDJDQHM GRNáDGQRFL ZyZF]DV QDVWSXMH ]PQLHj- V]HQLHMHJRUR]P\FLDSURSRUFMRQDOQLHGRSURFHQWRZHMZDUWRFLEádu. σ = σ λ 4σ

11 :DUWRüSDUDPHWUXλMHVWPDáDGODQRZ\FKZ]áyZJG\*WHGRSLHURDGDSWXMVLQDWo- PLDVWZSU]\SDGNXVWDUV]\FKZ]áyZSDUDPHWUWHQPDGX*ZDUWRü =XZDJLQDWR*HSRZVWDZDQLHQRZ\FKZ]áyZMDNUyZQLH*RSW\PDOL]DFMDZ]áyZLVWQLHM- F\FK]DOH*QH V RG NROHMQRFL SRGDZDQLD ZHNWRUyZ WUHQLQJRZ\FK QD ZHMFLH VLHFL]D ND*- G\PUD]HPJG\VLHüXF]RQDMHVWQDW\FKVDP\FKGDQ\FKRWU]\PXMHVLNRQILJXUDFMVLHFLNWó- UHUy*QLVLRGVLHELH:ZLNV]RFLSU]\SDGNyZWHUy*QLFHVQLHZLHONLHFRáDWZR]DXZD*\ü QD]ELRU]HWHVWRZ\PJG\*Z\QLNZSRV]F]HJyOQ\FKSUyEDFKQD]ELRU]HWHVWRZ\PMHVWEDUG]R SRGREQ\*G\]ELyUWUHQLQJRZ\MHVW MHGQDN QLHZLHONL ZDULDQFMD PRGHOX PR*H E\ü GX*D FR SU]HMDZLDVLGX*Uy*QLFZNODV\ILNDFMLQD]ELRU]HWHVWRZ\PGODSRV]F]HJyOQ\FKSUyE 3URVW\PVSRVREHPQDUR]ZL]DQLHWHJRSUREOHPXMHVW]DVWRVRZDQLHW]ZNRPLWHWXVLHFL0e- WRGDWDSROHJDQDW\P*HQDGDQ\P]ELRU]HWUHQLQJRZ\PXF]\VLVLHüZLHORNURWQLH0DMFM PRGHOLVLHFLNODV\ILNDFMLZHNWRUyZ]H]ELRUXWHVWRZHJRGRNRQXMHVLSU]H]JáRVRZDQLHZLk- V]RFLRZHZ\ELHUDMFNODVNWyUDQDMF]FLHMZ\VWSXMHOXESU]H]ZD*RQNRPELQDFMURz- ZL]D]SRV]F]HJyOQ\FKVLHFL[9]. Metoda ta powoduje znaczne zmniejszenie wariancji mo- GHOXLMDNSRND]XMHGRZLDGF]HQLHGRVNRQDOHQDGDMHVLGRVLHFL) Obroty :FHOXOHSV]HJRGRSDVRZDQLDZ]áyZVLHFLGRGDQ\FKZ)60VWRVXMHVLQHXURQ\NWyU\FK funkcje transferu w n Z\PLDURZHMSU]HVWU]HQLGDMPR*OLZRüREURWXUHDOL]RZDQ\FKSU]H]QLH KLSHUSRZLHU]FKQLVWDá\FKZDUWRFLF]\OLJUDQLFGHF\]MLZ\]QDF]RQ\FKSU]H]QHXURQ:\No- QDQLHSHáQHJRREURWXMHVWREOLF]HQLRZREDUG]RNRV]WRZQHLSRZRGXMHJZDáWRZQH]PQLHMV]e- QLH VL V]\ENRFL XF]HQLD'ODWHJR WH*]DVWRVRZDQR REURW\ EGFH]áR*HQLHP REURWyZ GZu- Z\PLDURZ\FK 'OD SU]\NáDGX SU]HGVWDZLRQ\ ]RVWDQLH REUyW Z SU]HVWU]HQL WUyMZ\PLDURZHM 1DMSLHUZGRNRQXMHP\REURWXXNáDGXZVSyáU]GQ\FKGODSLHUZV]\FKGZyFKZ\PLDUyZRNW α, w wyniku czego z wektora (X,Y) otrzymujemy wektor (X,Y ): ; FRVα = < VLQα VLQα ; FRVα < :QDVWSQ\PNURNX ; = ; ;< = < LSRZWDU]DP\RSHUDFMHW\PUD]HPXZ]JOGQLDMFNWβSRáR*HQLDGDQHJRZ]áDPLG]\WU]e- FLPZ\PLDUHPLSáDV]F]\]QX,Y:RJyOQ\PSU]\SDGNXFDáDSURFHGXUDSRZWDU]DQDMHVWGOD ZV]\VWNLFK NROHMQ\FK Z\PLDUyZ.W\ REURWX GOD SRV]F]HJyOQ\FK Z]áyZ XVWDODQH VSRd- F]DVXF]HQLDGODND*GHJRZ]áDQLH]DOH*QLH =PLDQDNWyZQDFK\OHQLDQHXURQXGRRGSRZLHGQLFKRVLQDVWSXMH]DND*G\PUD]HPJG\Zy- NRQ\ZDQDMHVWDGDSWDFMDSRáR*HQLDLLQQ\FKSDUDPHWUyZWHJRZ]áD1DMSLHUZZ\]QDF]DQHV SRV]F]HJyOQHNW\QDFK\OHQLDθZHNWRUDPDMFHJRVZyMSRF]WHNZURGNXZ]áDDZLFMHVW WRSRáo*HQLHWHJRZ]áDDNRQLHFZPLHMVFXJG]LH]QDMGXMHVLDNWXDOQ\SXQNWZHMFLRZ\Z

12 3U]\NáDGREUyFRQ\FKGZyFKQHXURQyZ ZLHORZ\PLDURZHMSU]HVWU]HQLZHNWRUZHMFLRZ\PR*HE\üWUDNWRZDQ\MDNRSXQNW1DVWSQLH DNWXDOQHNW\QHXURQXφ VSU]HVXZDQHZNLHUXQNXZ\]QDF]oQ\FKZDUWRFL φ = φ + γ(θ φ) parametr γ MHVWWRWHQVDPSDUDPHWUNWyU\Z\VWSLáSRGF]DVXF]HQLDUR]P\ü -H*HOL Z GDQ\FK Z\VWSXM Z\UD(QLH QDFK\ORQH VNXSLVND WR ZLNV]Rü NWyZ Z\]QDF]RQ\FK GODSRV]F]HJyOQ\FKZHNWRUyZZSDGDMF\FKGRWHJRZ]áDEG]LHGRVLHELHSRGREQ\FKSU]H] FRáDWZRMHVWX]\VNDüRSW\PDOQ\NW-HGQDNJG\QLHPDZ\Uy*QLRQHJRNLHUXQNXGODVNXSLVND WRQDVWSXMHFLJáD]PLDQDZDUWRFLNWDφFRPR*HSRZRGRZDüWUXGQRFLZXF]HQLXVL'OD VNXSLVN Z\]QDF]RQ\FK SRGF]DV LQLFMDOL]DFML VLHFL NW\ ]QDMGRZDQH V ]D SRPRF SURVWHM ; = D ; GRSDVRZDQHMQDSRGVWDZLHZV]\VWNLFKZHNWRUyZQDOH*F\FKGRWHJRZ]áDVWG L L poszczególne parametry a i = k k :VSyáF]\QQLNLWHUyZQHVWDQJHQVRZLNWDSRPLG]\JáyZQRVLVNXSLVNDDRVLX 1. Tak ZLFSoV]F]HJyOQHNW\PR*QDZ\]QDF]\ü]HZ]RUX X X k 1 k i X X k i k i φ k = arctan(a k ) 1RZ\ Z]Há NWyU\ SRZVWDMH SRGF]DV XF]HQLD PD SRF]WNRZR NW\ ]HURZH SRQLHZD*W\ONR MHGHQ ZHNWRU QDOH*\ GR WHJR Z]áD L MHVW RQ MHJR URGNLHP,QLFMDOL]DFMD ] XZ]JOGQLHQLHP QLH]DOH*Q\FKREURWyZGODSRV]F]HJyOQ\FKZ]áyZ MHVW EDUG]LHM SUHF\]\MQD QL*]DVWRVRZDQLH DQDOL]\F]\QQLNyZJáyZQ\FK3&$OXELQQ\FKJOREDOQLHRNUHORQ\FKWUDQVIRUPDFMLGDQ\FK 1DZHWMHOLZF]DVLHXF]HQLDSDUDPHWU\REURWXQLHSRGOHJDMDGDSWDFMLZDUWRZSURZDG]LüPa- FLHU]HREURWXZRSLVDQ\SRZ\*HMVSRVyE,QQHPHWRG\WZRU]HQLDREUyFRQ\FKNRQWXUyZGHFyzji opisano w pracy [5].

13 5.4. Optymalizacja :NRFRZ\PHWDSLHXF]HQLDW]QJG\RVLJQLWDMDNRüNODV\ILNDFML]JRGQDMHVW]SR*GDQ QDVWSXMHRSW\PDOL]DFMDSROHJDMFDQDRGU]XFHQLXZ]áyZNWyUHPDMEDUG]RPDáHUR]PLDU\ W]QGRNWyU\FKZSDGDQLHZLHONDOLF]EDQS OXE ZHNWRUyZ ] FLJX WUHQLQJRZHJR 3o- ZVWDMRQHQDVNXWHN*GDQLD]E\WZ\VRNLHMGRNáDGQRFLNODV\ILNDFMLOXEWH*QLHZ\VWDUF]DMFe- JRUR]P\FLDGX*\FKZ]áyZLVWQLHMF\FKZVLHFL-H*HOLSU]\F]\QWZRU]HQLDPDá\FKZ]áyZ MHVW ]E\W V]\ENLH LFK WZRU]HQLH WR SR LFK RGU]XFHQLX SUyED GRXF]HQLD LVWQLHMF\FK Z]áyZ VSRZRGXMH]ZLNV]HQLHLFKUR]P\ü:SU]HFLZQ\PSU]\SDGNXSRQRZQLH]RVWDQXWZRU]RQH PDáHZ]á\3UyEDRGU]XFDQLDLGRXF]DQLDSRZWDU]DQDMHVWNLONDNURWQLHSRF]\PHWDSXF]HQLD MHVW]DNRF]RQ\-DNRüNODV\ILNDFMLSRW\PHWDSLHPR*HE\üPQLHMV]DRG*GDQHMSRQLHZD* F]üZ]áyZ]RVWDáDRdrzucona. (WDSNROHMQ\WRNRFRZDRSW\PDOL]DFMDVLHFLSRNWyUHMQLHQDVWSXMHMX*GRXF]DQLH2GU]XFa- QH VZ]á\ NWyU\FK OLNZLGDFMD QLH SRZRGXMH ]PLDQ\ SR]LRPX DNWXDOQHM NODV\ILNDFML $E\ XQLNQüVSUDZG]DQLDND*GHJRZ]áD]RVREQDW]QRGU]XFDQLDJRLVSUDZG]DQLDNODV\ILNDFML QDFDá\P]ELRU]HWUHQLQJRZ\PFRE\áRE\EDUG]RNRV]WRZQHGODND*GHJRZHNWRUDWUHQLQJo- ZHJRREOLF]DQDMHVWDNW\ZDFMDZV]\VWNLFKZ]áyZL]DSDPLW\ZDQDZDUWRüDNW\ZDFMLZ]áD QDMEDUG]LHMZ]EXG]DMFHJRVL7HQZ]Há]RVWDMHZ\áF]RQ\:\V]XNLZDQ\MHVWNROHMQ\Z- ]HáQDMEDUG]LHMZ]EXG]DMF\VLL]DSDPLW\ZDQDMHVWZDUWRüMHJRZ]EXG]HQLD0DP\ZLF PDFLHU] ] OLF]E HOHPHQWyZ GZD UD]\ ZLNV] QL* OLF]ED ZHNWRUyZ Z FLJX WUHQLQJRZ\P QDWRPLDVWZDUWRFLW\FKHOHPHQWyZUyZQHVPDNV\PDOQ\PZ]EXG]HQLRPGODRGSRZLHGQLFK ZHNWRUyZWUHQLQJRZ\FK:PDFLHU]\WHMXVXZDP\MHGHQZ]Há'ODZHNWRUDGODNWyUHJRZ- ]HáWHQPLDáQDMZLNV]ZDUWRüDNW\ZDFMLZVWDZLDQDMHVWGRPDFLHU]\ZDUWRü]HUR1DVWp- QLHQDSRGVWDZLHSR]RVWDá\FKZDUWRFLZ\OLF]DQDMHVWMDNRüNODV\ILNDFML-H*HOLMDNRüNODVy- ILNDFML QLH SRJRUV]\áD VL WR DQDOL]RZDQ\ Z]Há MHVW XVXZDQ\ Z SU]HFLZQ\P SU]\SDGNX ZVWDZLDQHVGRPDFLHU]\SoSU]HGQLHZDUWRFL 5.5. Selekcja cech 'OD ND*GHJR]Z]áyZ XNU\W\FK PR*QD UyZQLH* ]DVWRVRZDü HOLPLQDFM FHFK. W tym celu Z\ELHUDP\NROHMQRZ]á\LGODND*GHJR]QLFKRGU]XFDP\]FLJXWUHQLQJRZHJRZHNWRU\NWó- UHGRGDQHJRZ]áDZSDGDMF]\OLNWyUHVSU]H]QLHJRNODV\ILNRZDQH0R*HP\WRXF]\QLü JG\* Z\áF]HQLH FHFK\ Z GDQ\P Z(OH ] XZDJL QD WR *H VWRVXMHP\ IXQNFMH VHSDURZDOQH PR*HE\üWUDNWRZDQHMDN ZVWDZLHQLH GR LORF]\QX ZDUWRFL D ZLF PDNV\PDOQHM ZDUWRFL DNW\ZDFMLGODGDQHJRZ\PLDUX0R*HWRVSRZRGRZDüW\ONR]ZLNV]HQLHDNW\ZDFMLZ]áDGOD ZV]\VWNLFKZHNWRUyZWUHQLQJRZ\FK1LHPR*HVLZLF]PLHQLüNODV\ILNDFMDZHNWRUyZNWyUH E\á\SRSUDZQLHNODV\ILNRZDQHERGODW\FKZHNWRUyZWHQZ]HáLWDNPLDáQDMZLNV]HZ]Eu- G]HQLH'ODWHJRREOLF]DP\PDFLHU]Z]EXG]HW\ONRGODSR]RVWDá\FKZHNWRUyZWUHQLQJRZ\FK.D*GD]FHFKGODGDQHJRZ]áD]RVWDMHNROHMQRRGU]XFDQD3RZRGXMHWRZ]URVWIXQNFMLDNWy- ZDFMLWHJRZ]áD-HOLDNW\ZDFMDWDGODZHNWRUyZ]LQQHMNODV\QL*RSW\PDOL]RZDQ\Z]HáQLH SU]HNUDF]D DNW\ZDFML Z]áyZ SRSUDZQLH MH NODV\ILNXMF\FK]DSLVDQ\FK Z WDEOLF\ DNW\ZDFML to taka cecha nie jest potrzebna. 3URFHGXU\ RGU]XFDQLD Z]áyZ RUD] HOLPLQDFML FHFK SRZWDU]DQH V WDN GáXJR D**DGHQ Z]Há QLHPR*HMX*]RVWDüRGU]XFRQ\$OWHUQDW\ZQDPHWRGDVHOHNFMLFHFKSROHJDMFDQDPRG\ILNDFML IXQNFMLEáGXRSLVDQD]RVWDáDZSUDF\[13].

14 5.6. Rozpoznawanie 7HVWRZDQLHVLHFL)60SROHJDQDZ\V]XNLZDQLXGODGDQHJRZHNWRUDZHMFLRZHJRZ]áDNWyU\ XOHJD QDMZLNV]HPX Z]EXG]HQLX :HNWRU ZHMFLRZ\ MHVW SU]\SLVDQ\ GR NODV\ NWyU UHSUe- ]HQWXMH QDMOHSV]\ QHXURQ -H*HOL MHGQDN *DGHQ ] Z]áyZ QLH XOHJD Z]EXG]HQLX ZyZF]DV wektor wejflrz\qlh]rvwdmhvnodv\ilnrzdq\ 'RRV]DFRZDQLD MDNRFL NODV\ILNDFML VáX* GZD SDUDPHWU\ ZDUWRü Z]EXG]HQLD RUD] ZVSyá- F]\QQLN ]DXIDQLD :DUWRü Z]EXG]DQLH G MHVW ] ]DNUHVX >@ LP MHVW ZLNV]D W\P ZHNWRU ZHMFLRZ\EOL*V]\MHVWLVWQLHMFHPXSUoWRW\SRZLNWyU\SRZVWDáSRGF]DVXF]HQLD :VSyáF]\QQLN ]DXIDQLD QDWRPLDVW PR*QD WUDNWRZDü MDNR SUDZGRSRGRELHVWZR SRSUDZQHJR zaklasyfikowania wektora wejflrzhjrx do danej klasy S N = & L & * ; ' σ &L N &L & ; S N * ; ' σ N & N & & L L L = :OLF]QLNXVXPRZDQLHSU]HELHJDSRZV]\VWNLFKZ]áDFKUHSUH]HQWXMF\FKNODV]Z\FL]F\Z PLDQRZQLNXVXPDELHJQLHSRZV]\VWNLFKZ]áDFKXNU\W\FK Z VLHFL :]á\ SU]HFKRZ\ZDü PRJUyZQLH*LQIRUPDFMHV\PEROLF]QHNWyUHPRJE\üSU]HGVWDZLDQHQDZ\MFLX 6. 3U]\NáDGRZHUH]XOWDW\ 'RWHVWRZDQLDVLHFL)60X*\WRVWDQGDUGRZ\FK]DJDGQLHNODV\ILNDF\MQ\FKZ]LW\FK]UHSozytorium baz danych Uniwersytetu Kalifornijskiego w Irvine [8] JG]LH ]QDOH(ü PR*QD Go- NáDGQLHMV]\RSLVGDQ\FK:V]\VWNLHSRQL*V]HSU]\NáDG\SU]HGVWDZLDMZ\QLNLNWyUHSRZVWDá\ ZZ\QLNXXUHGQLHQLDNLONXUH]XOWDWyZGODGDQHMED]\ :V]\VWNLH GDQH ]RVWDá\ QDMSLHUZ ]HVWDQGDU\]RZDQH : SRQL*V]\FK WDEHODFK SRGDQD ]RVWDáD SURFHQWRZDSRSUDZQRüNODV\ILNDFMLQD]ELRU]HWHVWRZ\POXEWH*MHOL]ELyUWHVWRZ\QLHZy- VWSRZDáSU]HGVWDZLRQ\MHVWZ\QLN]NURWQHMNURVZDOLGDFML:SU]\SDGNXJG\LVWQLDá\]e- EUDQHZ\QLNLUy*Q\FKNODV\ILNDWRUyZGODGDQHJR]ELRUX)60]RVWDáSRUyZQDQ\]QDMOHSV]y- PL]QLFK-HOLWDNLHZ\QLNLQLHLVWQLDá\GRNRQDOLP\SRUyZQDQLD)60]QDMOHSV]\PPRGe- OHP0/3MDNLXGDáRVL]QDOH(üZOLWHUDWXU]HE\áDWR]Z\NáDZVWHF]QDSURSDJD]FMD5SURS Quickprop lub dla danych hypothyroid genetyczna optymalizacja parametrów), metody QDMEOL*V]\FKVVLDGyZk-NN [9] oraz drzewa decyzji C4.5 [10]. We wszystkich tabelach re- ]XOWDW RWU]\PDQ\ ] VLHFL )60 SU]HGVWDZLRQ\ MHVW Z RVWDWQLHM NROXPQLH ZV]\VWNLH SR]RVWDáH UH]XOWDW\ V Z NROHMQRFL PDOHMFHM GRNáDGQRFL NODV\ILNDFML :H ZV]\VWNLFK SU]\SDGNDFK Z\QLNLRVLJQLWH]DSRPRF)60V]EOL*RQHGRQDMOHSV]\FK:LFHMZ\QLNyZ]QDOH(üPR*- na na stronie internetowej: 'DQH'1$]DZLHUDMZHNWRUyZZ]ELRU]HWUHQLQJRZ\PLZHNWRUyZZ]ELRU]H WHVWRZ\P :\VWSXMH ELQDUQ\FK DWU\EXWyZ L WU]\ NODV\ R QDVWSXMF\P UR]NáDG]LH procentowym: w zbiorze treningowym 23.2%, 24.3%, 52.5%, w zbiorze testowym 25.6%, 23.6%, 50.8%.

15 'RNáDGQRüQD zbiorze testowym Radial Dipol92 Alloc80 QuaDisc Discrim FSM 95.9% 95.2% 94.3% 94.1% 94.1% 94.3% 'DQHÄMRQRVIHUD ]DZLHUDM ZHNWRUyZ] F]HJR SLHUZV]\FK X*\ZD VL GR WUHQo- ZDQLDQDWRPLDVWSR]RVWDáHGRWHVWRZDQLD'DQHWHUHSUH]HQWXMV\JQDáUDGDURZ\RGELW\RG MRQRVIHU\.D*G\]ZHNWRUyZ]DZLHUDDWU\EXW\RZDUWRFLDFKFLJá\FK:\VWSXMGZLH NODV\ SLHUZV]D ZLDGF]FD R Z\VWSRZDQLX Z MRQRVIHU]H SHZQ\FK VWUXNWXU L GUXJD ZLDGF]FDREUDNX W\FK VWUXNWXU 2ELH NODV\ Z ]ELRU]H WUHQLQJRZ\P VSUDZLHUyZQoliczne. 'RNáDGQRüQD]ELRU]H testowym k-nn MLP C4.5 FSM 98.7% 96.0% 94.9% 97.7% 'DQH ÄK\SRWK\URLG ]DZLHUDM ZHNWRU\ Z ]ELRU]H WUHQLQJRZ\P L Z ]ELRU]H WHVWRZ\P6WRGDQH]GZyFKNROHMQ\FKODWEDGDSU]HVLHZRZ\FK]DZLHUDMFHLQIRUPa- FMHRQLHGRF]\QQRFLQDGF]\QQRFLOXEQRUPDOQLHG]LDáDMFHM WDUF]\F\ 3URFHQWRZ\ URz- NáDGW\FKWU]HFKNODVMHVWQDVWSXMF\ZSOLNXWUHQLQJRZ\PWHVWRZ\P :\VWSXMHDWU\EXWyZELQDUQ\FKLFLJá\FK 'RNáDGQRüQD]ELRU]H testowym C4.5 C-MLP2LN CART FSM 99.5% 99.36% 99.36% 99.1% 'DQHÄVDWLPDJH VNáDGDMVL]LQWHQV\ZQRFLSLNVHOL]QDMGXMF\FKVLZVVLHG]WZLH[ RWU]\PDQ\FK]F]WHUHFK]GMüVDWHOLWDUQ\FKZUy*Q\FK]DNUHVDFKVSHNWUDOQ\FKVWGZ\VW- SXMH DWU\EXWyZ PDMF\FK ZDUWRFL ] SU]HG]LDáX : ED]LH MHVW ZHNWRUyZ WUHQLQJRZ\FKLWHVWRZ\FK 'DQHSRG]LHORQHVQDV]Hü NODV FKRG]L R Uy*QH So- ZLHU]FKQLH RGELMDMFH PDMF\FK QDVWSXMF SURFHQWRZ OLF]HEQRü Z SRV]F]HJyOQ\FK zbiorach: zbiór treningowy 24.2%, 10.8%, 21.6%, 9.4%, 10,6%, 23.4%, testowym 23.1%, 11.2%, 19.9%, 10.5%, 11.8%, 23.5%. 'RNáDGQRüQD]ELRU]H testowym k-nn LVQ Dipol92 Radial FSM 90.6% 89.5% 88.9% 87.9% 89.8% 'DQHÄVRQDU ]DZLHUDMZHNWRUyZNWyUHSRG]LHORQHUyZQRQD]ELyUWUHQLQJRZ\LWe- VWRZ\:\VWSXMGZLHNODV\.D*G\]ZHNWRUyZSRVLDGDFLJá\FKDWU\EXWyZ&HOHP jest oduy*qlhqlhv\jqdáxvrqduxrgelwhjrrgphwdoxrgv\jqdáxrgelwhjrrgvndá\ 'RNáDGQRüQD]ELRU]H testowym MLP+BP k-nn C4.5 FSM 90.4% % 'DQHÄVKXWWOH ]DZLHUDMZHNWRUyZZ]ELRU]HWUHQLQJRZ\PLZ]ELRU]HWe- VWRZ\P:\VWSXMHVLHGHP NODV PDMF\FK QDVWSXMF\ XG]LDá SURFHQWRZ\ Z SRV]F]HJyl-

16 nych zbiorach: zbiór treningowy 78.41%, 0.09%, 0.3%, 15.51%, 5.65%, 0.01%, 0.03%, WHVWRZ\P'DQHSRVLDGDMFL- Já\FKDWU\EXWyZ 'RNáDGQRüQD]ELRU]H testowym NewId BayTree Cn2 Cal5 FSM 99.99% 99.98% 99.97% 99.97% 99.97% 'DQHÄOHWWHUV ]DZLHUDMZHNWRU\RSLVXMFHGX*\FKOLWHU]DOIDEHWXM]\NDDQJLHOVNLHJR :\VWSXMHZHNWRUyZ]F]HJRSU]H]QDF]RQ\FK]RVWDáRGRWUHQRZDQLDVLHFLD SR]RVWDáHGRWHVWRZDQLD'DQHWHXWZRU]RQH]RVWDá\]Uy*Q\FKIRQWyZ'RND*GHM OLWHU\ VSRUyG W\FK IRQWyZ GRGDQ\ ]RVWDá V]XP 8WZRU]RQR F]DUQR ELDáH SURVWRNWQH REUD]\NWyUHQDVWSQLHSU]HGVWDZLRQRZSRVWDFLZHNWRUDVNáDGDMFHJRVL] FHFK Qu- PHU\F]Q\FK :V]\VWNLH FHFK\ ]RVWDá\ SU]HVNDORZDQH WDN DE\ ZDUWRFL W\FK FHFK\ E\á\ FDáNRZLWHZ]DNUesie od 0 do 15. 'RNáDGQRüQD]ELRU]H testowym Alloc80 k-nn LVQ QuaDisc FSM 93.6% 93.2% 92.1% 88.7% 92.2% 'DQHÄJDOD[LHV ]DZLHUDMRSLVJDODNW\N]NDWDORJX(62/9[12]. Celem jest wykonanie automatycznej klasyfikacji, która porównywalna jest do klasyfikacji eksperta. Zbiór ten ]DZLHUD SRQDG ZHNWRUyZ 6LHü WUHQRZDQD MHVW QD ]ELRU]H ]DZLHUDMF\P HOe- PHQWyZLWHVWRZDQDQD]ELRU]HZHNWRUyZ.D*G\ZHNWRUVNáDGDVL]FHFKLPo- *HQDOH*HüGRMHGQHM]GZyFKNODVJDODNW\NLZF]HVQHJRW\SXOXEWH*JDODNW\NLSy(QHJR typu. 'RNáDGQRüQD]ELRU]HWHVWowym k-nn C4.5 MLP+BP FSM 92.82% 92.4% 89.6% 93% 'DQHÄKHSDWLWLV GRW\F]FKRUyEZWURE\RWU]\PDQH]7RNLMVNLHJRXQLZHUV\WHWXPHG\Fznego [13]'DQH WH]ZLHUDM SU]\SDGNyZ Z W\P X*\WH]RVWDá\ GR WHVWRZDQLD D SR]RVWDáHGRWUHQRZDQLDVLHFL.D*G\SU]\SDGHNRSLVDQ\]RVWDáSU]H]FHFK:\VWSXM klasy. 'RNáDGQRüQD]ELRU]HWHVWowym k-nn C4.5 MLP FSM 82.8% 75.5% 68% 82.2% Dane VHJPHQWDWLRQ ]DZLHUDMZHNWRUyZZ]ELRU]HWUHQLQJRZ\PLZ]ELRU]H WHVWRZ\P:\VWSXMHNODVND*GD]NODVZ]ELRU]HWUHQLQJRZ\PSRVLDGDZHNWRUyZD Z]ELRU]HWHVWRZ\P:V]\VWNLHZHNWRU\RSLVDQHVSU]H]FHFKRZDUWRFLDFKFL- Já\FK

17 'RNáDGQRüQD]ELRU]HWHVWowym k-nn C4.5 MLP FSM 90.33% 89.8% 88.33% 91.2% 'DQHÄEUHDVWFDQFHUZLVFRQVLQ ]DZLHUDMSU]\SDGNyZZUyGNWyU\FKZ\VWSXMH FKRU\FK RUD] ]GURZ\FK SU]\SDGNyZ.D*G\ SU]\SDGHN RSLV\ZDQ\ MHVW SU]H] FHFK PDMF\FKZDUWRüZ]DNUHVLHRG'ODSU]\SDGNyZMHGQDZDUWRüMHVWEUDNXMFD: miejvfdzduwrfleudnxmfhmzvwdzlrqd]rvwdádzduwrüuhgqldgodgdqhmfhfk\ 'RNáDGQRüREOLF]RQD] krotnej kroswalidacji IncNet k-nn FDA FSM 97.1% 97.1% 96.8% 96.5% Dane appendictis [14]]DZLHUDMSU]\SDGNyZRSLVDQ\FK]DSRPRFFHFK:\VW- SXMGZLHNODV\PDMFHQDVWSXMF\XG]LDáSURFHQWRZ\ 'RNáDGQRüREOLF]RQD] krotnej kroswalidacji k-nn MLP C4.5 FSM 89.3% 83.9% 83.5% 84.2% 7. Podsumowanie &KRFLD*RSLVDQ\WXDOJRU\WPZ\GDZDüVLPR*HSRF]WNRZRVNRPSOLNRZDQ\LWUXGQ\ZX*y- FLXZU]HF]\ZLVWRFLZ\NRQXMHVLQLHPDODXWRPDW\F]QLHQLHZ\PDJDMFLQJHUHQFMLX*\WNRw- QLNDZSURFHVXF]HQLDVLOXEZ\ELHUDQLDDUFKLWHNWXU\ 6LHüVWDUWXMH]SURWRW\SyZXWZRU]RQ\FKSRGF]DVJUXSRZDQLDDQDVWSQLHGRGDMHMHOLMHVWWR NRQLHF]QHQRZHQHXURQ\'RGDQLHQRZ\FKQHXURQyZX]DOH*QLRQHMHVWRGRGOHJáRFLPLG]\ ZHNWRUHP]QDMGXMF\PVLQDZHMFLXVLHFLLDNWXDOQ\PLSURWRW\SDPLXWZRU]RQ\PLSU]H]VLHü RUD]RGUHDNFMLVLHFLQDWHQZHNWRUZ]EXG]HQLDLVWQLHMF\FKZ]áyZ3RF]WNRZHSURWRW\S\ ]QDMGRZDQHV]DSRPRFZVWSQHMLQLFMDOL]DFMLRSDUWHMQDJUXSRZDQLX,QLFMDOL]DFMDWDNDSo- ]ZDOD Z\VWDUWRZDü ] RSW\PDOQ\FK SURWRW\SyZ FR SRZRGXMH F]VWR SU]\VSLHV]HQLH SURFHVX XF]HQLDRUD]XWZRU]HQLHVLHFL R QLHZLHONLHM OLF]ELH Z]áyZ 7DN ZLF FDáD DUFKLWHNWXUD VLHFL ]DOH*\W\ONRLZ\áF]QLHRGGDQ\FKNWyUH]RVWDMX*\WHGRMHMXF]HQLD 3R]DDUFKLWHNWXUDLVWRWQ\PF]\QQLNLHP ZSá\ZDMF\P QD MDNRü NODV\ILNDFML MHVW ]GROQRü Z\WZDU]DQLD SU]H] PRGHO Uy*QRURGQ\FK REV]DUyZ GHF\]\MQ\FK SU]\ XWU]\PDQHM VHQVRZQHM ]ár*rqrflwhjrprghox:ádvqrüwdxpr*olzldohsv]hgrsdvrzdqlhvlnodv\ilndwrudgrga- Q\FKDFR]DW\PLG]LHRVLJQLFLHOHSV]HMJHQHUDOL]DFML :VLHFL)60]PLDQNV]WDáWXREV]DUyZGHF\]\MQ\FKPR*QDX]\VNDüSRSU]H]VWRVRZDQLHUy*- Q\FKIXQNFMLDNW\ZDFMLRUD]PR*OLZRüZ\NRQDQLDREURWyZZZLHORZ\PLDURZHMSU]HVWU]HQL 6WRVRZDQLHUy*Q\FKIXQNFMLDNW\ZDFMLRWZLHUDUyZQLH*Uy*QHGURJLDQDOL]\GDQ\FKQSLQWHr- SUHWDFM]DSRPRFUHJXáORJLF]Q\FKZ\VWDUF]\ZW\PFHOX]DVWRVRZDüIXQNFMHSURVWRNWQH SU]HFKRG]F VWRSQLRZR RG IXQNFML ELFHQWUDOQ\FK OXE JDXVVRZVNLFK F]\ WH* LQWHUSUHWDFM RSDUWRORJLNUR]P\WIXQNFMDWUyMNWQDJDXVVRZVND7D JLWNRü WZRU]HQLD Uy*Q\FK Rb- V]DUyZGHF\]\MQ\FKXPR*OLZLD]DVWRVRZDQLHVLHFL)60ZZLHOXG]LHG]LQDFKFRSRWZLHUG]DM przedstawione wyniki.

18 =DVWRVRZDQLDWHJRPRGHOXGRDSURNV\PDFMLMDNRSDPLFLDVRFMDF\MQHMRUD]MDNRIXQNFMLKHu- U\VW\F]QHM Z SUREOHPDFK RSW\PDOQHJR VSHáQLDQLD ZLHOX RJUDQLF]H [1] QLH ]RVWDá\ MHV]F]H SRGMWH 3RG]LNRZDQLD =D ZVSDUFLH ILQDQVRZH Z UDPDFK JUDQWX QU 7) MHVWHP\ ZG]LF]QL.RPLWHWRZL%DGD1DXNowych. Literatura [1] Duch W., Diercksen G. H. F. (1995): Feature Space Mapping as a universal adaptive system. -- Computer Physics Communications, Vol 87, pp [2] Duch W. (1997): Platonic model of mind as an approximation to neurodynamics. [w:] Brainlike computing and intelligent information systems (S-i. Amari, N. Kasabov, Ed.). Singapore Springer, rozdz. 20, s [3] Bishop C. (1995): Neural network for pattern recognition. Oxford: Clarendon Press. [4] Duch W. (1996): From cognitive models to neurofuzzy systems - the mind space approach. -- Systems Analysis-Modeling-Simulation, Vol. 24, pp [5] Duch W., Jankowski N. (1999): Survey of neural transfer functions -- Neural Computing Surveys, Vol. 2, pp [6] Duch W., Adamczak R., Jankowski N. (1997): Initialization of adaptive parameters in density networks -- Third Conference on Neural Networks and Their Applications, Kule, SD(G]LHUQLN 1997, s [7] Kohonen T. (1995): Self-organizing maps. -- Heidelberg Berlin: Springer-Verlag. [8] Blake C. L. and Merz C. J. (1999), UCI repository of machine learning databases [9] 'XFK : *UXG]LVNL. The weighted k-nn method with selection of features and its neural realization th Conference on Neural Networks and Their Applications, Zakopane, Maj 1999, s [10] Quinlan J. R. (1993): C4.5: Programs for machine learning.-- Morgan Kaufmann, San Mateo, CA. [11] 'XFK : $GDPF]DN 5 *UEF]HZVNL. Methodology of extraction, optimization and application of crisp and fuzzy logical rules. -- IEEE Transactions on Neural Networks special issue on Data Mining. [12] Lahav O., Naim A., Sodre L. Jr. and Storne-Lombardi M. C. (1995): Neural Comptutation as a tool for galaxy classification: methods and examples. -- Institute od Astronomy, Cambridge, Technical report CB3 OHA. [13] Duch W., Adamczak R., Grbczewski K., )DO * +D\DVKL < Fuzzy and crisp logical rule extraction methods in application to medical data. -- Computational Intelligence and Applications (P.S. Szczepaniak. Ed.) Springer, Studies in Fuzziness and Soft Computing, Vol. 23. [14] Weiss S.M., Kapouleas I. (1990): An empirical comparison of pattern recognition, neural nets and machine learning classification methods. [w:] Readings in Machine Learning (Shavlik J.W. and Dietterich T.G. Ed.). -- Morgan Kauffman Publ, CA. [15] Churchland P.S., Sejnowski T.J. (1992): The computational brain. -- MIT, Bradford Book. [16] Thelen E., Smith L.B. (1994): A Dynamic Systems Approach to the Development of Cognition and Action. -- MIT Press. [17] Breiman L. (1998): Bias-variance, regularization, instability and stabilization. -- Neural Networks and Machine Learning (Bishop C. M. Ed.), s Springer-Verlag.